Kagiyama began to skate at the age of 5. He is currently coached by his father, Masakazu Kagiyama.
2018–2019 season
Kagiyama's coach, father Masakazu, was ill for part of the season and could not work on coaching the technical aspects. He instead spent time working with choreographer Misao Sato to improve his expression during this period. Kagiyama opened his season at the 2018 Asian Open Trophy, where he won the junior title ahead of teammate Tatsuya Tsuboi. He placed fourth at his first Junior Grand Prix event, 2018 JGP Canada. Kagiyama won his first JGP medal, a silver, at 2018 JGP Armenia. He placed fifth at the 2018–19 Japan Junior Championships, and as a result, was invited to the senior championships. Kagiyama placed sixth at the senior level and was chosen as the first alternate for the 2019 World Junior Championships team. He competed as a senior at the 2019 International Challenge Cup and won the silver medal behind teammate Sōta Yamamoto.
2019–2020 season
Kagiyama won gold at 2019 JGP France with a new junior world record for the combined score. His total was 34.16 points higher than that of silver medalist Aleksa Rakic of Canada. His quadruple toe loop in the free skate set the junior record for the highest valued single jump, before being surpassed by Daniel Grassl's quadruple lutz at 2019 JGP Italy. Kagiyama set a new junior world record in the free skating at 2019 JGP Poland, and surpassed his junior world record for the total score. However, he eventually won silver behind Daniil Samsonov of Russia, who broke his junior world records for the free skating and the total score after Kagiyama skated. Kagiyama's results qualified him to the 2019–20 Junior Grand Prix Final, where he placed fourth. Kagiyama won gold at the 2019–20 Japan Junior Championships by over 37 points ahead of Shun Sato and Lucas Tsuyoshi Honda. As junior national champion, Kagiyama was named to represent Japan at the 2020 Winter Youth Olympics and the 2020 World Junior Championships. He was also invited to compete in the senior division at the 2019–20 Japan Championships, alongside the rest of the top six finishers in the junior division. Competing at the 2019–20 Japan Championships, Kagiyama placed seventh in the short program and second in the free skate, to win the senior national bronze medal. He was not selected to compete at the 2020 World Championships, but was assigned as one of Japan's three entries at the 2020 Four Continents Championships, in addition to his previously-earned berth to the 2020 World Junior Championships. Kagiyama was chosen by the Japanese Olympic Committee as the flag-bearer for the Japanese national team at the 2020 Winter Youth Olympics. He won gold at the 2020 Winter Youth Olympics ahead of Russians Andrei Mozalev and Daniil Samsonov. Kagiyama was selected by draw to be a member of Team Focus for the team event. He won the men's free skating portion to help Team Focus win the silver medal. At the Four Continents Championships, Kagiyama scored a personal-best 91.61 in his short program, beating his old mark by almost seven points and placing fifth in the segment. He rose to the bronze medal overall in the free skate, his first senior ISU championship medal, calling it "a precious time and experience. I was able to get closer to what I wanted to achieve." Finishing the season at the 2020 World Junior Championships, Kagiyama won the short program ahead of Andrei Mozalev. After opening his free skate with a fall on a quad toe loop, he performed the remaining jumps successfully until singling a planned triple Axel as his closing jump, and placed fifth in that segment. He remained narrowly in second place overall, ahead of Petr Gumennik, and won the silver medal. Speaking afterward, he said "I felt like my body and my mind were not connected" and attributed the errors to that.
Records and achievements
Set the junior-level men's combined total record at 2019 JGP France. Later surpassed by Kagiyama himself at 2019 JGP Poland, before being surpassed by Daniil Samsonov at the same event.
Set the junior-level men's free skating record at 2019 JGP Poland. Later surpassed by Daniil Samsonov at the same event.
