Aitcheson's father, Joe Sr., who went by his middle name Leiter, also pitched for the Baltimore Orioles in the minor leagues and the Brooklyn Dodgers in the majors, helped his brother Whitney found the Iron Bridge Hounds, serving as its Master of Foxhounds for many years.
Aitcheson enlisted in the United States Navy, serving four years during the Korean War as a gunner’s mate on the aircraft carrier USS Oriskany.
The National Steeplechase Association has maintained, since 1956, a list of annual leading jockeys by races won.
Aitcheson rode many of his era's national champions including Peal (1961), Amber Diver (1963), Bon Nouvel (1964, 1965, 1968), Tuscalee (1966), Top Bid (1970) and Soothsayer (1972).
In 1976, he became the only professional jockey to receive the National Steeplechase Association's F. Ambrose Clark Award for lifetime service to the sport.