Joseph was born on the 27th of November 1876, in Philadelphia, Pennsylvania, and while information of his life is scarce, it is known that he enlisted in the US Navy and was deployed to China on board the USS Newark. It was his actions as a Gunner’s Mate First Class that would later earn him the Medal of Honor. The citation reads:

In the presence of the enemy during the battle of Peking, China, 12 July 1900, Mitchell distinguished himself by meritorious conduct.

Joseph received the Medal on the 19th of July 1901, and he reached the rank of Lieutenant. Joseph Andrew Mitchell died on the 9th of June 1925, at the age of 48, and he is buried with his wife, Alice, in the All Saints Catholic Cemetery in Portsmouth, Virginia: Section E1, Lot 4 (Bourke Lot).