<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-04-16</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0000791915</issuerCik>
        <issuerName>CYPRESS SEMICONDUCTOR CORP /DE/</issuerName>
        <issuerTradingSymbol>CY</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001722181</rptOwnerCik>
            <rptOwnerName>GEHA SAM</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>198 CHAMPION COURT</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>SAN JOSE</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>95134</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>EVP, Memory Products</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2020-04-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>199426</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.85</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable>
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                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1084</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.85</value>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
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            <exerciseDate>
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            </exerciseDate>
            <expirationDate>
                <footnoteId id="F3"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1084</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
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                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
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            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>14861</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.85</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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                <footnoteId id="F5"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F5"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>14861</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
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        </derivativeTransaction>
        <derivativeTransaction>
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                <value>Restricted Stock Units</value>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>32504</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.85</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
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            <exerciseDate>
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            <expirationDate>
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                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>32504</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
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                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Restricted Stock Units</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-04-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>69294</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>23.85</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F7"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F7"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>69294</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On April 16, 2020 (the &quot;Effective Time&quot;), pursuant to the Agreement and Plan of Merger, dated as of June 3, 2019 (the &quot;Merger Agreement&quot;), by and among Cypress Semiconductor Corporation (the &quot;Issuer&quot;), Infineon Technologies AG (&quot;Infineon&quot;) and IFX Merger Sub Inc. (&quot;Merger Sub&quot;), Merger Sub merged with and into the Issuer, with the Issuer as the surviving entity and a wholly owned subsidiary of Infineon.  Pursuant to the Merger Agreement, each outstanding share of the Issuer's common stock (&quot;Common Stock&quot;) was converted into the right to receive $23.85 per share in cash (the &quot;Per Share Merger Consideration&quot;), without interest.</footnote>
        <footnote id="F2">Restricted stock units convert into common stock on a one-for-one basis upon settlement.</footnote>
        <footnote id="F3">On July 8, 2015, the Reporting Person was granted 5,418 restricted stock units that vest in five equal annual installments beginning on June 22, 2016.</footnote>
        <footnote id="F4">Pursuant to the Merger Agreement, immediately prior to the Effective Time, each outstanding restricted stock unit award, whether vested or unvested, was cancelled and converted into the right to receive a cash payment equal to the product of (i) the number of restricted stock units subject to such award immediately prior to the Effective Time multiplied by (ii) the Per Share Merger Consideration.  Such payment is to be made at the times and subject to any vesting and acceleration conditions set forth in the Merger Agreement.</footnote>
        <footnote id="F5">On February 16, 2018, the Reporting Person was granted 44,582 restricted stock units that vest in three equal annual installments beginning on the first anniversary of the grant date.</footnote>
        <footnote id="F6">On February 15, 2019, the Reporting Person was granted 56,340 restricted stock units, with approximately 42% of the units vesting on the first anniversary of the grant date and the remainder of the units vesting in equal installments on the second and third anniversaries of the grant date.</footnote>
        <footnote id="F7">On March 1, 2020, the Reporting Person was granted 69,294 restricted stock units that vest in three equal annual installments beginning on February 14, 2021.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Pamela L. Tondreau, attorney-in-fact</signatureName>
        <signatureDate>2020-04-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
