Born in Kamloops, BC, Grimson was originally drafted by the Detroit Red Wings in 1983 before re-entering the draft in 1985 and being selected by the Calgary Flames 143rd overall. After he scored 24 goals and racked up 248 penalty minutes for the WHL's Regina Pats in 1984-85, Grimson spent two years at the University of Manitoba. "The Grim Reaper" began his pro career with the IHL's Salt Lake City Golden Eagles, while playing a handful of games in Calgary but the Flames were deep at forward and placed him on waivers.

Grimson was claimed by the Chicago Blackhawks and went on to play three years for the team. In 1992 he dressed for 14 playoff games while providing grit on the club when it reached the finals for the first time in 19 years. In June, 1993, Grimson was selected by the Mighty Ducks of Anaheim in the Expansion Draft. He provided leadership for nearly two years before joining the powerful Detroit Red Wings to add depth to their roster.

The Hartford Whalers picked up Grimson on waivers early in the 1996-97 and he remained with the franchise when it relocated to Carolina the next season. After two years back in Anaheim, Grimson helped the Los Angeles Kings make the playoffs in 2000-01 and upset the Detroit Red Wings in the first round.

Following a one year stint with the Kings, Grimson joined the Nashville Predators who were looking for a physical presence up front. However, since his arrival with the Preds' Grimson has been plagued with injuries and has played only 30 games over the past two seasons.