Cutter was born in Skellefteå, Sweden where his dad Sean, a former professional goaltender, played for two seasons. Shortly thereafter, Cutter and his family returned to the United States where Cutter began his hockey journey playing for the Honeybaked program. Cutter was selected to the US National Development Team to begin the 2020-21 season where he played for two seasons. As a result of his strong play, Cutter was drafted 5th overall in the 2022 NHL Entry Draft by the Philadelphia Flyers. The following season, Cutter began his NCAA career at Boston College. In his freshman season he led the Eagles in goals and points and was recognized as a unanimous selection to the Hockey East All-Rookie Team and Third Hockey East All-Star Team. Cutter represented his country twice in that same season representing the United States at the World Junior Championships where he won a bronze medal and again at the World Championships scoring 7 goals in 10 games as the youngest forward on the team. Cutter returned to Boston College for his sophomore season recording 38 goals to lead the NCAA while totalling 65 points in 41 games. He was recognized as one of the three finalists for the 2024 Hobey Baker Award and was named to the All-Hockey East First Team as well as being named an ACHA First Team All-American. He was also named USA Hockey’s Jim Johannson College Player of the Year. Cutter once again represented the United States at the World Junior Championship this time winning a Gold Medal while being named the tournament’s best forward. The Anaheim Ducks acquired Cutter’s rights following a trade with the Philadelphia Flyers on January 8, 2024. The Ducks then signed Cutter to a three-year entry-level contract following his sophomore season at Boston College. Cutter made his NHL debut on April 4, 2024 notching an assist in a win over the Vegas Golden Knights.