Stop Military Selective Service Registration Act This bill repeals the Military Selective Service Act, which requires most men of ages 18 through 25 years old to register with the Selective Service System in case a draft is reinstated. The assets, contracts, property, unexpended balances and records held by the Selective Service System must be transferred to the Office of Selective Service Records (reestablished by this bill) upon the repeal. The bill prohibits the reenactment of the Military Selective Service Act or reestablishment of the Selective Service System unless there is a vote by two-thirds of each chamber of Congress.