Selected by New Jersey Devils round 1 #2 overall 1984 NHL Entry Draft.
"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 Stephane 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, as he was shocked 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, they recalled him, but Muller 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. Muller had his last 20 goal season with the 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.
Received this black sharpie signed card IP at the Gretzky Tennis tourney.