Butcher played college hockey at the University of Denver from 2013 to 2017. For his play in the 2016–17 season, Butcher won the Hobey Baker Award as the best player in men's college hockey.[3] He was also named a NCHC First-Team All-Star, NCHC Player of the Year, and NCHC Offensive Defenseman of the Year for 2016–17.[4] He helped Denver win the 2017 NCAA Championship.[5]
On August 27, 2017, as an NHL free agent, Butcher signed a two-year, entry-level maximum contract with the New Jersey Devils worth an annual base salary of $925,000.[6]
After participating in his first training camp with the Devils, Butcher made the Devils' opening night roster for the 2017–18 season.[7] In the Devils' home opener, Butcher made his NHL debut against the Colorado Avalanche on October 7, 2017, a game in which he became the first Devils' player in franchise history to record three points in his debut, registering three assists on the power play in a 4–1 victory.[8]
On July 31, 2019, Butcher signed a three-year contract extension with the Devils.[9] On February 18, 2020, Butcher suffered a season-ending injury during the game between the Devils and St. Louis Blues. He appeared in 56 games, recording four goals and 17 assists during the 2019–20 season.[10][11]
After completing his fourth season with the Devils, and with his role diminishing in each season, Butcher was traded by New Jersey along with a fifth-round draft pick in 2022 to the Buffalo Sabres on July 28, 2021 for future considerations, in a move to clear cap space for the Devils.[12] In the 2021–22 season, Butcher saw his offensive impact decrease for the fifth consecutive season, collecting two goals and eight points in just 37 games with the Sabres.
At the conclusion of his contract with Buffalo, Butcher was signed as a free agent to a one-year, two-way contract with the Dallas Stars on July 22, 2022.[13] In the following 2022–23 season, Butcher was assigned to the AHL for the first time in his career, joining affiliate the Texas Stars. He remained in Texas for the duration of his contract, leading the blueline in scoring with 43 points while setting a franchise record with 37 assists for a defenseman in a single season.
As a free agent from the Stars, Butcher was signed to a one-year, two-way contract with the Pittsburgh Penguins on July 3, 2023.[14] However, halfway through the season, Butcher was traded to the Minnesota Wild in exchange for forward Maxim Čajkovič.[15][16]
At the conclusion of his contract with the Wild, Butcher left as a free agent and signed his first contract abroad, agreeing to a one-year deal with Kazakhstan-based club Barys Astana of the Kontinental Hockey League (KHL) on July 25, 2024.[17][18] In the 2024–25 season, on October 18, Butcher was released by the team following just 15 appearances along with fellow North American ex-NHLers Michael McLeod and Nathan Beaulieu.[19]