Giammalva won the ATP tournament in Napa as an amateur in 1980 and became a professional tennis player in the same year. As a professional, he was in the final in Houston the following year , where he was defeated by Guillermo Vilas . He also stood at the side of his brother Tony in the Atlanta finals . In 1983 he won his second and last individual title in Monterrey .
In the doubles competition he won four titles and was in 13 other finals. He won the title in Tokyo alongside his brother Tony. He had his best placement in the tennis world rankings in singles with position 28 in 1985 and in doubles in 1984 with position 22.
His best individual result at a Grand Slam tournament was reaching the quarter-finals of Wimbledon in 1982. In the doubles competition, he was also able to reach the quarter-finals of Wimbledon in 1983.