Private First Class Mitchell was a member of Company F, 2nd Battalion, 24th Infantry Regiment, 25th Infantry Division. He was listed as Missing in Action while fighting the enemy in South Korea on 4 December 1950 and returned to duty on 21 December 1950. He was listed as Missing in Action again on 8 January 1951. He was presumed dead on 31 March 1954. His remains were not recovered. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Mitchell was awarded the Purple Heart, the Combat Infantryman Badge, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.