 Selected in the 1987 NHL Entry Draft by the Minnesota North Stars, Kaminski only played one game for the North Stars before he was traded to the Quebec Nordiques in exchange for Gaetan Duchesne.After spending several years in the Nordiques organization, principally for their Halifax Citadels AHL team, he was traded to the Washington Capitals prior to the 1993–94 NHL season.During his four seasons with the Capitals, his hard-nosed style of play would make him a fan favorite, as he would not hesitate to fight players much bigger than he was.