He played in the NHL for 19 seasons from 1984–85 until 2002–03 with the Dallas Stars, Florida Panthers, New Jersey Devils, New York Islanders, Toronto Maple Leafs and won the Stanley Cup in 1993 as member of the Montreal Canadiens.

Ultimately, Muller was traded at a discount to the Toronto Maple Leafs, in a three team trade that saw Muller and Don Beaupre go 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.

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.

)[4] Muller began his coaching career with the Queen's University Golden Gaels in his hometown of Kingston.

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.

[5] On June 27, 2011, the Nashville Predators announced that Muller had been hired as the head coach of their AHL affiliate, the Milwaukee Admirals.

[10] On August 13, 2020, Muller temporarily replaced head coach Claude Julien who was hospitalized with chest pains.