Good Samaritan Cleanup of Abandoned Hardrock Mines Act of 2013 - Encourages the partial or complete remediation of inactive and abandoned mine sites for the public good by good samaritans (defined as individuals or entities who had no role in the creation of the historic mine residue or any resulting environmental pollution and are not legally responsible for the remediation of the historic mine residue). Defines "inactive or abandoned mine site" as a mine site located in the United States that is no longer actively mined and that was used for the production of a mineral other than coal and has historic mine residue. Amends the Federal Water Pollution Control Act (commonly known as the Clean Water Act) to authorize a permitting authority (i.e., the Administrator of the Environmental Protection Agency [EPA] or a state or Indian tribe with an approved good samaritan program) to issue good samaritan discharge permits. Sets forth requirements for the issuance of such permits, including the applicant's submission of a detailed remediation plan and a determination by a permitting authority that such plan preserves water quality. Grants a release from liability under such Act to good samaritans who comply with a discharge permit approved under the terms of this Act. Terminates the authority to issue good samaritan discharge permits ten years after enactment of this Act.