Acquired via waivers in 1998, Jassen Cullimore contributed seven solid, if not spectacular, seasons to the Tampa Bay Lightning. He was originally drafted with the 29th selection of the 2nd round of the 1991 NHL Entry Draft by the Vancouver Canucks. He spent parts of three seasons (including a 33 game stretch with the Syracuse Crunch) in the AHL before sticking with the Canucks. In 1996, he was traded to the Montreal Canadiens for Donald Brashear. After being waived by the Canadiens, Cullimore skated in 408 games for the Lightning, third all-time among Lightning defenders and is one of only 11 players to log over 400 games with Tampa Bay. His final game with the Lightning was Game 7 of the 2004 Stanley Cup playoffs.
Afterward, Cullimore signed as a free agent with the Chicago Blackhawks and later went on to the Florida Panthers before announcing his retirement after the 2011-12 season, which he spent with Iserlohn in Germany. As a member of the Lightning, Cullimore posted 15 goals and 38 assists for 53 total points and 396 penalty minutes during regular season play. In his 22 postseason games with the team over the 2002-03 and 2003-04 seasons, he chipped in with a goal and three assists with 10 penalty minutes.
Following his retirement, Cullimore and his family settled in the Tampa Bay area where he is active as a coach in local youth hockey. He has also started doing some work with the Lightning's TV and radio broadcasters.