Nuclear Waste Cleanup Act - Declares that, with respect to material stored at a Department of Energy (DOE) site at which activities are regulated by the State of South Carolina, high-level radioactive waste does not include radioactive material resulting from the reprocessing of spent nuclear fuel that the Secretary of Energy determines: (1) does not require permanent isolation in a deep geologic repository for spent fuel or highly radioactive waste; (2) has had highly radioactive radionuclides removed in accordance with Nuclear Regulatory Commission-reviewed criteria; and (3) in the case of material derived from storage tanks, is disposed of in a facility (including a tank) within South Carolina.

Exempts from this Act any such material transported from South Carolina.

Authorizes DOE to implement any action authorized by a State-approved closure plan or State-issued permit in existence on the date of this Act.