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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001441236</issuerCik>
        <issuerName>Clearwater Paper Corp</issuerName>
        <issuerTradingSymbol>CLW</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001184292</rptOwnerCik>
            <rptOwnerName>HUNT KEVIN J</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>601 WEST RIVERSIDE AVE.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 1100</rptOwnerStreet2>
            <rptOwnerCity>SPOKANE</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>99201</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Phantom Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>19.14</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2019-05-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5224.66</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>19.14</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F2"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>5224.66</value>
                    <footnoteId id="F3"/>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>18531.63</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Phantom stock units are credited to the reporting person's account on the transaction date in accordance with the provisions of the Clearwater Paper Corporation Deferred Compensation Plan for Directors and will be converted to cash and paid on a 1-for-1 basis with the issuer's common stock.</footnote>
        <footnote id="F2">Phantom stock units will be converted to cash and paid upon the reporting person's termination from service with Clearwater Paper in accordance with the provisions of the Clearwater Paper Corporation Deferred Compensation Plan for Directors.</footnote>
        <footnote id="F3">Phantom stock unit beneficial ownership represents phantom stock allocated to the reporting person's Deferred Compensation Account since the reporting person's last report.  These phantom stock allocations represent an annual award grant for service from May 1, 2019 through April 30, 2020.  These phantom stock units will vest May 1, 2020.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Carol K. Haugen, Attorney-in-Fact</signatureName>
        <signatureDate>2019-05-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
