A Providence man through and through, Hassett was a high-school legend at LaSalle High School in Providence before continuing on to Providence College. With the Friars, Hassett's shooting ability earned him the nickname "Sonar". He averaged 18.1 points per game during his senior season.

Hassett spent two years in Seattle, with the team advancing to the NBA Finals both years, and averaged 4.0 points in 103 games as a backup guard on a team deep at the position. He shot 47.4% during his second season despite taking so many of his shots from long range. During the 1978-79 season, Hassett was the only NBA player to spend the entire season active and not miss a free throw, hitting 23-for-23 from the line.

Hassett took advantage of the three-point line to bolster his career after the Sonics released him the fall after the championship. He was fourth in the NBA with 69 threes during the 1979-80 season after signing with the Indiana Pacers. During 1980-81, while playing for Dallas and Golden State, Hassett was second in the league in threes made and three-point percentage, canning 53 at a 34.0% clip. He again finished second by making 71 threes during the 1981-82 season, his last one as a regular.

Hassett finished his career with three seasons in Golden State. He finished with a career scoring average of 5.9 points per game, with a high of 8.7 in 1980-81. He hit 194 career three-pointers and made 33.6% of his attempts from downtown as well as 86.1% at the free-throw line.

Hassett was named to Sports Illustrated's list of Rhode Island's 50 greatest athletes in the 20th century. He was also inducted into the New England Basketball Hall of Fame in 2003. He still resides in the Providence area, where he provides color commentary for Friars games in addition to working as an Investment Banker for Fleet Financial Group.