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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-03-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000352363</issuerCik>
        <issuerName>Kate Spade &amp; Co</issuerName>
        <issuerTradingSymbol>KATE</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001601368</rptOwnerCik>
            <rptOwnerName>Lloyd Deborah J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O KATE SPADE &amp; COMPANY</rptOwnerStreet1>
            <rptOwnerStreet2>2 PARK AVE</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10016</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Creative Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Market Share Units</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>21027</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $1 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>21027</value>
                    <footnoteId id="F1"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>21027</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
        <derivativeTransaction>
            <securityTitle>
                <value>Performance Share Units</value>
                <footnoteId id="F2"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F2"/>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2016-03-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>63082</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common stock, par value $1 per share</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>63082</value>
                    <footnoteId id="F2"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>63082</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each Market Share Unit (&quot;MSU&quot;) represents the right to receive one share of common stock based on certain vesting conditions. The number of MSUs reported represents the target number awarded on March 2, 2015. This 2015 MSU award, by its terms, became effective upon satisfaction of a material non-market price condition. The actual number of shares of common stock that may vest is contingent on the market price levels that the Issuer's common stock achieves during pre-determined intervals, with a potential payout ranging from 30% to 200% of the number of target MSUs awarded. 50% of this 2015 MSU award will vest, if at all, after each of the following performance periods ending on:
March 2, 2017 and March 2, 2018.</footnote>
        <footnote id="F2">Each Performance Share Unit (&quot;PSU&quot;) represents the right to receive one share of common stock based on certain vesting conditions. The number of PSUs reported equals the target number awarded on March 2, 2015. This 2015 PSU award, by its terms, became effective upon satisfaction of a material non-market price condition. The actual number of shares of common stock that may vest, if any, is contingent on the Issuer's Cumulative Adjusted EBITDA and Average Cumulative Adjusted EBITDA Margin % achieved over the three year period from 2015 through 2017, adjusted to reflect the Issuer's total shareholder return (&quot;TSR&quot;) performance relative to that of all companies in the S&amp;P MidCap 400, with potential to earn a number of shares of common stock between 0% and 250% of the target number of PSUs awarded. This 2015 PSU award will cliff vest, if at all, after the performance period ending December 30, 2017.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Timothy Michno, as Attorney-In-Fact</signatureName>
        <signatureDate>2016-03-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
