Mann completed his secondary education at Dixie Heights High School before attending Harvard University on a Navy ROTC scholarship, graduating "cum laude" in 1961 with a degree in biochemical science. After graduating, Mann served in the United States Navy from 1961 to 1965. As a lieutenant, Mann served aboard the destroyer USS "English" during the Cuban Missile Crisis. Mann was a supporter of President John F. Kennedy; Mann credits Kennedy's assassination with convincing him to attend law school instead of medical school so that he could better engage in public service. After his time in the navy, Mann attended Harvard Law School and was awarded a Bachelor of Laws degree in 1968.