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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-04-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001754874</rptOwnerCik>
            <rptOwnerName>Bowden Steve M</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>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Senior Vice President</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2020-04-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>30594</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.75</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>39425</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents award of restricted stock units (&quot;RSUs&quot;) granted in connection with the leadership transition at Clearwater Paper Corporation and previously described in a Form 8-K filed by the Company on January 31, 2020.  RSUs may be settled only for shares of common stock on a one-for-one basis.</footnote>
        <footnote id="F2">Represents award of RSUs that will vest on April 1, 2022, assuming continued employment.  During the vesting period, an amount equal to the dividends that would have been paid on the RSUs had they been in the form of common stock will be converted into additional RSUs.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Michael S. Gadd, Attorney-in-Fact</signatureName>
        <signatureDate>2020-04-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
