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.
Mitchell served as the Cherokee Judicial Circuit solicitor general from January 1, 1953, until December 31, 1956 and as a judge in that circuit's Superior Court from January 1, 1957, until January 8, 1958. Upon the 1957 death of U.S. Representative Henderson Lovelace Lanham from the Georgia's 7th congressional district, Mitchell ran as a Democrat and won the special election to fill Lanham's term in the 85th United States Congress. He won re-election in 1958 and did not seek re-election in 1960. After his political service, Mitchell returned to his law practice in Dalton and currently resides there (as of 2008).