Sweeney was born in Concord, Massachusetts, but grew up in Boxborough, Massachusetts. He was drafted out of high school by the Boston Bruins in the 1982 NHL Entry Draft, and went on to play four years at Boston College. He made his NHL debut in the 1986–87 season, but spent most of the year with the Bruins AHL affiliate the Moncton Golden Flames. The 1987–88 season was Sweeney's first full year, a season where Boston traveled to the Stanley Cup Finals only to be swept by the Edmonton Oilers. Following six seasons with Boston, Sweeney was claimed off waivers by the Buffalo Sabres in 1992 and then by the New York Islanders in 1995. After being traded to the Calgary Flames during the 1995–96 season Sweeney retired from the NHL. He spent the next season in the IHL before traveling across the Atlantic to play in the Deutsche Eishockey Liga from 1997 until 2001. He is currently the head coach of the Valley Jr. Warriors '96 Elite squad. Bob Sweeney is the brother-in-law of Madeline Amy Sweeney, one of the flight attendants on American Airlines Flight 11, which hit the north tower of the World Trade Center during the September 11, 2001 attacks.
