Müller started the European Cup for the first time in Haus im Ennstal in December 2007 and finished 27th in the giant slalom. She made her debut in the snowboard world cup at the beginning of the 2008/09 season in Arosa and achieved 46th place in the parallel giant slalom. In the further course of the season she reached her first podium finishes in the European Cup in Adelboden with two second places in the parallel slalom. In the 2009/10 season she came on the podium four times in the European Cup. She won her first European Cup victory in the parallel slalom in Protasiv Yar and at the end of the season reached fourth place in the parallel ranking of the European Cup. In the following season, she placed 13 times in the top ten in 16 European Cup appearances, including two third places, one second place and two wins. She thus achieved second place in the parallel ranking. At the Snowboard Junior World Championships 2011 in Chiesa in Valmalenco she won the silver medal in the parallel giant slalom. At the beginning of the 2011/12 season , she got three points in the World Cup. In the further course of the season she reached eight podium finishes in the European Cup, including four victories and thus won the parallel ranking. At the World Cup in Moscow , she came fifth in the parallel slalom for the first time among the top ten in the World Cup. At the Snowboard Junior World Championships 2012 in Sierra Nevada , she won the silver medal in the parallel slalom and in the parallel giant slalom. In the 2012/13 season she started eight times in the World Cup. With fourth place in the parallel giant slalom in Carezza, she achieved her best position in the World Cup so far. At the season highlight of the 2013 Snowboard World Championships in Stoneham , she finished 12th in the parallel giant slalom and 11th in the parallel slalom. She finished the season in 19th place in the Parallel Slalom World Cup, 18th in the Parallel World Cup and tenth in the Parallel Giant Slalom World Cup. In April 2013 she became Swiss champion in the parallel giant slalom. Her best World Cup result in the following season was 15th place in the parallel slalom in Bad Gastein . At the 2014 Winter Olympics in Sochi , she came 18th in the parallel slalom and 17th in the parallel giant slalom. The following year she achieved 22nd place in the parallel giant slalom at the 2015 Snowboard World Championships on Kreischberg . In the 2015/16 season she took tenth place in the parallel ranking and fifth place in the parallel slalom ranking in the European Cup, and eighth place in the parallel ranking and seventh place in the parallel giant slalom ranking in the 2016/17 season. At the Snowboard World Championships 2017 in Sierra Nevada she came 13th in the parallel giant slalom.
Müller has taken part in 50 World Cup races so far and was among the top ten five times. (Status: end of season 2016/17)