After winning the "player of the year" award with the Spruce Grove Midget AAA team, Stevenson joined the Bonnyville Pontiacs of the Alberta Junior Hockey League (AJHL) for the 1999–00 season.

Playing with former Minnesota State Mavericks teammate Shane Joseph signed to a PTO contract March 15, Stevenson garnered five goals and 11 assists in 14 games.

Stevenson's powerful chemistry with Joseph helped earn him a contract with the Barons' NHL team, the San Jose Sharks.

[3] For the season 2009–10, Stevenson left North America and signed a one-year contract with Swiss team EHC Kloten of the National League A on June 24, 2009.

On July 29, 2010, Stevenson opted for his second foray into Europe signing as a free agent with German team Augsburger Panther of the DEL.