Career
Mueller began playing professionally with Eisbären Berlin of the Deutsche Eishockey Liga in the 2005-2006 season. He played with Berlin and their junior team in the third-level Oberliga for two seasons. He then joined the Kölner Haie in 2007.
The 2009-2010 season was his most successful season in the DEL scoring wise with the Kölner Haie accounting for 56 points in 53 games during the regular season.
He has also received a career high total of 122 penalty minutes. Müller was selected to play for the German national team for the 2010 Winter Olympics.
On July 14, 2010, Mueller signed a two-year entry level contract with the Toronto Maple Leafs. In his first season, after initially being assigned to affiliate, the Toronto Marlies for the 2010-2011 season, Mueller was recalled and on January 15, 2011 he played his first National Hockey League regular season game, a shootout loss to Calgary at home.
Unable to establish a role with the Maple Leafs, on July 20, 2012, Mueller left to sign with the MoDo Hockey of the Swedish Elitserien.
In signing with Modo, Mueller also became the franchise"s inaugural German player. After one season with Modo, Mueller returned to his native Germany and signed with former club, Kölner Haie on June 28, 2013. On April 28, 2015, Mueller signed a three-year contract as a free agent to join his fourth DEL team, the Hamburg Freezers.