Cassady played football for the Ohio State Buckeyes from 1952 to 1955. During his college career, he scored 37 touchdowns in 36 games. He also played defensive back; a pass was never completed on him in his four years at the university. He was twice selected as a consensus All-American, in 1954 and 1955. The 1954 Buckeyes finished the season 10–0 and won a consensus national championship. That year Cassady finished third in the vote for the Heisman Trophy, behind Alan Ameche of Wisconsin. In 1955, he won the Heisman Trophy (by the largest margin at the time) and the Maxwell Award, and was named the Associated Press Athlete of the Year. During his playing days, he was 5'10" and 170 pounds.