Sunset Wasteful Executive Expenditures and Programs Act of 2013 - Requires the Comptroller General (GAO): (1) each year, beginning in 2014, to review three executive departments to identify agencies and programs that perform similar or related functions and that no longer serve a public need; (2) to review every executive department at least once every five years; and (3) each year, beginning on February 1, 2015, to report to Congress on the results of the reviews of executive departments carried out during the preceding year with recommendations for abolishing agencies and programs that perform similar or related functions and no longer serve a public need.

Abolishes by December 31 of each year, beginning with 2015, the three executive departments reviewed by the Comptroller General during the preceding year. Requires the President to direct procedures for the winding down of the operations of each abolished department. Allows Congress to authorize the continued existence of an executive department scheduled for abolishment.

Sets forth the process for congressional consideration of the Comptroller General's report, including an expedited procedure for consideration of resulting legislation to be known as a wasteful expenditures bill.