Mueller was drafted 8th overall by the Phoenix Coyotes in the 2006 NHL Entry Draft. He plays as a center. He played in the USA Hockey developmental program for the 2004–05 season before moving to the Western Hockey League's Everett Silvertips. He followed former Breck High School teammate Blake Wheeler to the Coyotes, making the transition into the NHL during the 2007–08 season. Because of his outstanding performances in the first half of the 2007–08 season, Mueller was selected to play in the 2008 NHL YoungStars Game in Atlanta. He netted his first career NHL hat-trick against the Anaheim Ducks on November 7, 2007.