Mura comes from a family of figure skaters. Both parents were active in single and pair skating in the 1980s . His father Takashi Mura is his trainer.
In 2009, Mura reached the podium for the first time in the Japanese Senior Championships in third place and qualified for a world championship for the first time . There he finished 15th on his debut. It was not until 2013 that Mura was able to prevail again against the strong competition from home and secure participation for the world championship again as third in the national championships. In London , Canada , he finished eighth. Already in the Grand Prix series before Mura had demonstrated his improving form when he with the victory at the Trophée Eric Bompard his first Grand Prix competition could win. In 2014 Mura won the four continents championships in Taipei .