Muller started his junior career with the Kingston Canadians of the Ontario Hockey League, but his most successful junior seasons were with the Guelph Platers. There was a dispute in 1984 between the Platers and the Canadian Olympic Team, who wanted Muller to play with them at the 1984 Winter Olympics. The Platers owner was upset over losing Muller for so much time, but eventually they came to an agreement and Muller played in the Olympics. He was drafted second overall by the New Jersey Devils in the 1984 NHL Entry Draft behind Mario Lemieux. "Captain Kirk" was the heart and soul of the Devils franchise, with his intensity and strong two-way play. However, New Jersey never became a serious Stanley Cup contender while Muller was with them, and he was traded along with Roland Melanson to the Montreal Canadiens for Stéphane Richer and Tom Chorske on September 20, 1991.