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. Muller quickly became a fan favourite in Montreal, and he helped them win the Stanley Cup in 1993. However, his time with the Canadiens was shorter than he would have liked, when he was traded to the New York Islanders during the 1994–95 NHL season. Initially, he was reluctant to report to the Islanders, then played a handful of games in an uninterested manner before team management decided that his poor attitude outweighed his potential contributions on the ice and barred him from the team. Eventually, the Islanders recalled Muller, but he refused to report, freeing the Islanders from their contractual obligations to pay him. Ultimately, Muller was traded at a discount to the Toronto Maple Leafs, in a three team trade that saw Muller and Don Beauprego to the Maple Leafs, Martin Straka, Ken Belanger and the rights to Bryan Berard go to the Islanders while Damian Rhodes and the rights to Wade Redden went to the Ottawa Senators. Muller had his last 20 goal season with the Maple Leafs the next season, but he was traded to the Florida Panthers as the Leafs fell out of the playoff picture. Muller struggled in Florida, scoring just four goals in the whole 1998–99 NHL season. His last break came when he signed with the Dallas Stars in the middle of the 1999–2000 season. Even though his scoring touch of old almost completely evaporated, he still managed to be a strong role player with the Stars for four seasons and was part of the "grumpy old men" line that included Mike Keane and John MacLean. He retired at the end of the 2002–03 season.
Coaching career
Muller began his coaching career with the Queen's UniversityGolden Gaels in his hometown of Kingston. During 2005-06, Muller's Golden Gaels posted an 8-13-1-2 record in the Ontario University Athletics Conference. Muller also held the title of assistant coach to Marc Habscheid with Team Canada, winning the gold medal at the 2005 Lotto Cup Tournament in Slovakia. In March 2006, he served as assistant coach to Greg Gilbert at the Under-18 World Championship. Muller returned to the Montreal Canadiens organization on June 20, 2006, when he was named assistant coach of the Canadiens. On June 27, 2011, the Nashville Predators announced that Muller had been hired as the head coach of their AHL affiliate, the Milwaukee Admirals. On November 28, 2011, Muller became coach of the Carolina Hurricanes, taking over for Paul Maurice. On May 5, 2014, Muller was relieved of his coaching duties by the Carolina Hurricanes. On May 13, 2014, Muller was signed by the St. Louis Blues as an assistant coach. On June 2, 2016, the Montreal Canadiens organization rehired Muller as an associate coach.
Records
New Jersey Devils franchise record for points in a single game
New Jersey Devils franchise record for assists in a single game
New Jersey Devils franchise record for points by a centre in a single season
