Mitchell was born in Dalton, Georgia and attended the Citadel in Charleston, South Carolina. From 1943 through 1946, he served as a first lieutenant in the United States Army Air Corps. He also served in the United States Air Force in 1951 and 1952. Between his years of service in the two military branches, Mitchell attended the University of Georgia School of Law in Athens and earned LL.B. in 1948. He was admitted to the bar on April 17, 1948, and practiced law in Dalton.