[1] Mueller was drafted by the Hartford Whalers after a successful season of junior hockey and began attending Clarkson University the following fall.

For his sophomore season Mueller increased his point total and helped the Golden Knights win the conference tournament.

While the Lakers weren't as good as the year before, they were battle tested and the team managed to fight back against Clarkson and win a hard-fought road game 5–4.

He was named Vice President of Hockey operations for a program in the Chicago area and led teams to two national junior championships in 2012 and 2016.

After the second title, Mueller was hired by the Pittsburgh Penguins as a head coach and executive director of the UPMC Lemieux Sports Complex Hockey Academy and continues to work in that role as of 2021.