Puc won bronze with Yugoslavia at the 1988 Summer Olympics in Seoul, was with Croatia when they won gold at the 1996 Summer Olympics in Atlanta and played for Slovenia in Sydney in 2000 as the team finished 8th.

He began his career in Slovenia's Sostanj, but also played for Borac from Banja Luka in Bosnia-Herzegovina and Croatia's handball club Zagreb, winning two European champions titles.

He also played for the Slovenian clubs Celje Pivovarna Laško and Prule, winning the 2002 national championship with the latter.

Puc played 34 times for the Slovenian handball team scoring 120 goals.

He was also very successful in his appearances for Croatia; aside from the Olympic gold, he won silver at the 1995 World Championship and bronze at the 1994 European Championships.

Puc spent the last years of his life in Florida, where his son Borut attends the Nick Bollettieri Tennis Academy. He had been fighting against cancer after the disease spread from the lungs to the liver.