In 225 career National Hockey League regular-season games, the 6-foot-2, 205-pound Beaulieu owns 60 points (seven goals, 53 assists), adding four points in 17 career playoff games.
The 24-year-old Strathroy, Ont., native was drafted by the Canadiens in 2011 with the 17th overall pick.
All of a sudden, Montreal's left side defensive depth has taken a major hit with Beaulieu gone as well as top prospect Mikhail Sergachev who was dealt in exchange for Jonathan Drouin back on Thursday.
Beaulieu spent his first five seasons with Montreal.
"Obviously, it's disappointing", Beaulieu said of being a healthy scratch against NY, per the Montreal Gazette. Montreal lost that game 3-1 at Madison Square Gardens and lost the series 4-2.
On Sunday at 10:30am, the National Hockey League announced which players each team had chosen to protect from the upcoming expansion draft.
Beaulieu immediately improves the Sabres' blue line under new coach Phil Housley, a Hall of Fame defenseman.