Caviezel, who competes for SC Rätia Chur, has been taking part in the European Cup since 2010. He has achieved ten podium finishes so far, four of them victories. In the 2014/15 season, he finished second in the parallel ranking (as of the end of the 2017/18 season).
He made his debut in the Snowboard World Cup in December 2012 in Carezza , which he finished in 37th place in the parallel giant slalom. At the 2014 Junior Snowboarding World Championships in Chiesa in Valmalenco , he was sixth in the parallel giant slalom and in the parallel slalom. In the following year he won the silver medal in the parallel giant slalom at the Snowboard Junior World Championships in Yabuli and also achieved fourth place in the parallel slalom. After finishing 33rd at the World Cup in Carezza at the beginning of the 2016/17 season, he achieved his first top ten placement in the World Cup in Cortina d'Ampezzo with fourth place in the parallel slalom. This was followed by four more top ten results and at the end of the season the tenth place in the parallel giant slalom world cup, the ninth place in the parallel slalom world cup and the eighth place in the parallel world cup. At the season highlight of the 2017 Snowboard World Championships in Sierra Nevada , he finished 26th in the parallel slalom and 19th in the parallel giant slalom. In the 2017/18 season he achieved two top ten placements, including third place in the parallel giant slalom in Carezza, 20th place in the parallel world cup. At the 2018 Winter Olympics in Pyeongchang , he came 22nd in the parallel giant slalom. At the end of March 2018, he became Swiss champion in parallel slalom in Davos .
In the following season 2018/19 Caviezel achieved third place in the parallel giant slalom in Scuol and second place each in the parallel slalom in Bad Gastein and Moscow , thus reaching 11th place in the parallel world cup and third place in the parallel slalom world cup. In addition, he and Patrizia Kummer took third place in the team competition in Bad Gastein . At the season highlight, the Snowboard World Championships 2019 in Park City , he finished ninth in the parallel slalom and eighth in the parallel giant slalom. In the 2019/20 season he was third in Scuol and third in the team competition in Bad Gastein.