Cohen began his lacrosse career in 1960 at Long Island's Baldwin High School, where he was named All-County twice and captain of the 1961 team. As an attackman at Cornell University, he was first team All-American in 1966 and third team All-American in 1965. In 1963, 1965 and 1966 he led the Ivy League in scoring, was named first team All-Ivy, and selected as Cornell's most valuable player. He was the captain of Cornell's 1966 Ivy League championship team.
A veteran club player for Long Island Lacrosse Club and the New York Athletic Club, Cohen was named to the United States Club Lacrosse Association's All-Club team nine times in his ten-year club career. In 1974, Cohen was selected to the U.S. Team, which successfully defended its World Championship in Melbourne, Australia. Cohen was inducted into Cornell's Athletic Hall of Fame in 1982 and into the Long Island Metro Lacrosse Hall of Fame in 1987.