Murk made her debut in the Freestyle World Cup on November 23, 2003 in Saas-Fee , where she finished 8th and won her first World Cup points. The first podium placement followed on February 21, 2004 with 3rd place in Naeba . In the winter of 2004/05 it was not enough to make it onto the podium, but she achieved a top 10 placement four times. A 6th place was the best result in the 2005/06 World Cup season. Murk achieved his last podium finish on January 10, 2007 in Flaine . With a total of three top 10 placements, she took 4th place in the ski cross discipline of the World Cup. At the 2007 World Championships in Madonna di Campiglio , she made it to the final run, but narrowly missed a medal in fourth.
During the 2007/08 season Murk was in the top ten four times in World Cup races. She could not maintain this level in the 2008/09 season due to various injuries, the best results were two 12th places. Further injuries in the first half of the 2009/10 season meant that she could not qualify for the Winter Olympics. At the first post-Olympic World Cup race, she returned the favor with 6th place, the best result of the winter. In 2011 Murk only took part in one World Cup race. After the Swiss championships on April 2, 2011, she resigned from top-level ski cross sports.
On March 2nd, 2015, she made her comeback in the SDH speed skiing discipline in Grandvalira / Andorra. There she won gold at the world championships and secured the world championship title on her debut. At the World Cup on the following day, she finished 2nd.
At the Speedmasters race on April 3, 2015 in Vars / France, she set a new Swiss record with 196,507 km / h.