Cupit played on the PGA Tour from 1961 to 1973 and had four victories. His first came at the Canadian Open in 1961, helping him to win the PGA's Rookie of the Year award. His last tour win came in 1966 at the Cajun Classic. Cupit's best finish in a major was runner-up at the U.S. Open in 1963, when he and Arnold Palmer lost to Julius Boros in a three-way playoff.
After reaching the age of 50 in 1988, Cupit played part-time on the Senior PGA Tour. He currently is the Golf Professional Emeritus at the Links at Land's End in Yantis, Texas.[1]