Beecher is a product of the United States Development Team Program (USHL). In 2018-19, the 18-year-old produced 6 goals and 14 assists for 20 points in 27 games. The 6-foot-3, 209-pound forward recorded 25 points (9g, 16a) and a plus-11 rating in 34 games during the 2017-18 season with the USNTDP. In 2016-17, the Elmira, New York native skated in 30 games, accumulating 12 goals and 12 assists for 34 points at the Salisbury School (USHS-Prep) in Connecticut.
Beecher won a bronze medal with Team USA at the 2019 U18 World Junior Championship where he recorded three goals and one assist for four points and a plus-four rating in seven games. He won a gold medal at the 2018 U17 World Hockey Championship, scoring one goal in six games. He is committed to the University of Michigan for the 2019-20 season.