Thompson Divide Withdrawal and Protection Act of 2013 - Withdraws the Thompson Divide Withdrawal and Protection Area (the Thompson Divide) in Colorado from: (1) entry, appropriation, and disposal under the public land laws; (2) location, entry, and patent under the mining laws; and (3) operation of the mineral leasing, mineral materials, and geothermal leasing laws.

Directs the Secretary of the Interior to provide a written notice to holders of valid existing mineral leases or other mineral interests within the Thompson Divide of the potential opportunity for donation, voluntary exchange, or other relinquishment of those rights for retirement.

Permits a holder of a valid mineral lease or other mineral interest within the Thompson Divide, upon receipt of such notification, to submit a written notice to the Secretary of that holder's interest in the retirement or other conveyance of such right for withdrawal and protection purposes.

Instructs the Secretary to prepare a list of interested holders and make such list available to the Secretary of Agriculture (USDA), qualified nonprofit conservation organizations, or persons interested in acquiring a right for retirement.

Requires, if any mineral lease or other mineral interest is relinquished, donated to, exchanged, or otherwise acquired by the United States within the Thompson Divide or under the authority of the Secretary or the USDA Secretary, such land to be withdrawn as described above.

Prohibits the Secretaries from using federal funds to repurchase valid federal mineral leases or other mineral interests within the Thompson Divide.