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

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-03-25</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001001838</issuerCik>
        <issuerName>SOUTHERN COPPER CORP/</issuerName>
        <issuerTradingSymbol>PCU</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001042701</rptOwnerCik>
            <rptOwnerName>Grupo Mexico, S.A.B. de C.V.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>CAMPOS ELISEOS NO. 400</rptOwnerStreet1>
            <rptOwnerStreet2>COLONIA LOMAS DE CHAPULTEPEC</rptOwnerStreet2>
            <rptOwnerCity>MEXICO CITY, MEXICO</rptOwnerCity>
            <rptOwnerState>O5</rptOwnerState>
            <rptOwnerZipCode>11000</rptOwnerZipCode>
            <rptOwnerStateDescription>MEXICO</rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001251594</rptOwnerCik>
            <rptOwnerName>AMERICAS MINING CORP</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>11811 NORTH TATUM BLVD.</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 2500</rptOwnerStreet2>
            <rptOwnerCity>PHOENIX</rptOwnerCity>
            <rptOwnerState>AZ</rptOwnerState>
            <rptOwnerZipCode>85028</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2009-03-25</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>200000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>17.87</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>679500000</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                    <footnoteId id="F2"/>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnote</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These shares were purchased in multiple transactions at prices ranging from $18.49 to $17.42, inclusive. The reporting persons undertake to provide to Southern Copper Corporation, any security holder of Southern Copper Corporation or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares purchased at each separate price within the ranges set forth in footnote 1 to this Form 4.</footnote>
        <footnote id="F2">Americas Mining Corporation (&quot;AMC&quot;) directly owns 679,500,000 shares of Common stock. AMC is owned by Grupo Mexico, S.A.B. de C.V.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Daniel Muniz Quintanilla, Chief Financial Officer of Grupo Mexico, S.A.B. de C.V.</signatureName>
        <signatureDate>2009-03-26</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>/s/ Daniel Muniz Quintanilla, Vice-President and Chief Financial Officer of Americas Mining Corporation</signatureName>
        <signatureDate>2009-03-26</signatureDate>
    </ownerSignature>
</ownershipDocument>
