Károly Hauszler began his sports career in 1964 as a swimmer at the Central Sports School. He was not found to be talented enough in this sport, however, so he was recommended to join the water polo team. From 1970 he was a goalkeeper for Bp. Honvéd, then between 1978 and 1988 for Tatabányai Bányász. Between 1974 and 1981 he played in 56 matches for the national team. As a member of the Hungarian national team, Hauszler won the European Youth Championship title in 1971, won the World Cup in 1979, and won the bronze medal with the national team at the 1980 Olympics in Moskva.
In 1984 Hauszler obtained a coaching certificate at the College of Physical Education, and from 1988 he worked as a coach of the Tatabánya team. In 1995 he moved to Esztergom where he served as the water polo coach of the Esztergom Waterball Sport Club from 2000, and then of the Új-Hullám Sport Association in Dorog in 2013.