Prior to turning professional, Butcher played four seasons at the University of Denver from 2013-17. In 158 career collegiate games, he recorded 28 goals, 75 assists and 103 points, and captained his team to the NCAA Championship in his senior season in 2016-17. That season, he received the Hobey Baker Award as the NCAA's top collegiate player, as well as USA Hockey's College Player of the Year Award after ranking third among league defensemen in assists (30) and second in points (37).