[1] He played in the National Hockey League with the Boston Bruins, Los Angeles Kings, and Florida Panthers between 1992 and 2008.

Internationally Stümpel played for the Slovak national team at several tournaments, including the 2002, 2006, and 2010 Winter Olympics, and eight World Championships, winning a gold in 2002.

Prior to the 2004–05 NHL lockout season, Stümpel had played for only two clubs, the Bruins and the Los Angeles Kings.

On May 4, 2011, Stümpel moved from the Kontinental Hockey League (KHL)'s Dinamo Minsk to Spartak Moscow.

A long-time friend of Žigmund Pálffy since the beginning of their professional careers, they were often line-mates on the Slovak national team.