He ranks among the top ten in many Bruins team statistics, including fourth overall in total games played.

[2] Sweeney made his NHL debut during the 1988–89 season, having spent half of the year with the American Hockey League (AHL)'s Maine Mariners.

In the following season, he helped the Bruins in the NHL to win the Prince of Wales Trophy by scoring six points in 21 games until they eventually lost to the Edmonton Oilers in the Stanley Cup Finals.

He retired with NHL totals of 52 goals and 221 assists for 273 points and 681 penalty minutes in 1,115 career regular season games.

Shortly after, he traded long-time Bruins forward Milan Lucic to the Los Angeles Kings in exchange for the 13th overall pick (used to select Jakub Zbořil), Martin Jones and Colin Miller.

Four days later, on June 30, Sweeney then traded Jones to the San Jose Sharks for a first-round pick in 2016 (29th overall, used to select Trent Frederic) Sweeney guided the Bruins return to prominence in the 2018–19 season, winning the Eastern Conference Finals and securing a berth at the 2019 Stanley Cup Finals against the St. Louis Blues.