Carl Mitchell was born on September 2, 1928, in South Bend, Indiana. He entered the U.S. Military Academy at West Point on July 1, 1946, and graduated with a commission as a 2d Lt in the U.S. Air Force on June 2, 1950. Lt Mitchell next completed Undergraduate Pilot Training and was awarded his pilot wings at Vance AFB, Oklahoma, in August 1951. He completed B-29 Superfortress Combat Crew Training in January 1952, and then served with the 5th Bomb Squadron at Travis AFB, California, from February 1952 to July 1953, and he then transferred with the squadron to Mountain Home AFB, Idaho, where he served as a B-47 Stratojet pilot from July 1953 to September 1959. Capt Mitchell next received an Air Force Institute of Technology assignment to complete his Master's degree in Aerospace Engineering at the University of Michigan from September 1959 to September 1961, followed by service as a research and development analyst with the Ballistic Systems Division at Los Angeles, California, and then at Norton AFB, California, from September 1961 to August 1963. Maj Mitchell began flying combat missions as a B-26B Invader pilot with the 1st Air Commando Squadron at Bien Hoa AB, South Vietnam, in November 1963, and was killed in action on January 14, 1964. His remains have never been recovered.

His Air Force Cross Citation reads:

Major Carl B. Mitchell distinguished himself by extraordinary heroism in connection with military operations against an opposing armed force as an Advisor-Pilot of a B-26B aircraft on 14 January 1964. On that date, Major Mitchell voluntarily exposed himself and his aircraft during low level flight over hidden Viet Cong machine gun installations. Despite heavy machine gun fire, which repeatedly struck his aircraft, Major Mitchell aggressively continued his efforts to locate and destroy the machine gun installations until his badly damaged aircraft crashed and burned. Through his extraordinary heroism, superb airmanship, and aggressiveness, Major Mitchell reflected the highest credit upon himself and the United States Air Force.