Mast enlisted in the United States Army Reserve in May 2000 and went to become a combat engineer. In 2006, he transitioned to the active U.S. Army and became an explosive ordnance disposal technician. Mast later joined the elite 28th Ordnance Company. He served in Afghanistan as part of Operation Enduring Freedom. On September 19, 2010, while clearing a path for United States Army Rangers in Kandahar, Mast took a wrong step into an IED along the road. The explosion resulted in the amputation of both his legs and one of his fingers.
On June 8, 2015, Mast announced his candidacy for the Republican nomination United States House of Representatives in Florida's 18th congressional district. Mast faced five opponents in the August 30, 2016, primary; he won.