Cohen was born in Brooklyn, New York, and was Jewish. His brother Herb Cohen competed at the 1961 Maccabiah Games in Israel, won the NCAA foil championship in 1961-62, won a bronze medal in individual foil and a gold medal with the US foil team at the 1963 Pan American Games, was Amateur Fencers League of America (AFLA) foil champion in 1964, and fenced individual and team foil for the United States in the 1964 Summer Olympics.