Mulloy was a 1936 graduate of the University of Miami, and tennis coach at the school. He also was a member of Lambda Chi Alpha fraternity. He recruited to Miami and played doubles with George Toley, who went on to win 10 NCAA team titles at the University of Southern California. Probably Mulloy's greatest contribution to tennis was advancing the popularity of senior tennis. He played the senior circuit around the world into his nineties, and established the Mulloy Cup for international competition between men tennis players 80 years of age and over. He won over 127 national championships and 25 international titles in 75 years of playing competitive tennis.