Kagiyama is the former world junior record holder for the free skate and combined total score under the ISU Judging System.

[12] Kagiyama slowly started to make a name for himself and won the gold in the Novice A Class at the 2014 Kanto Regional Figure Skating Championships at the age of 11.

Kagiyama won gold at the 2019–20 Japan Junior Championships by over 37 points ahead of Shun Sato and Lucas Tsuyoshi Honda.

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.

[31] Finishing the season at the 2020 World Junior Championships, Kagiyama won the short program ahead of Andrei Mozalev.

[35] In the free skate, he landed three quads cleanly, with his only error being singling a planned triple loop in a combination, but outscored second-place Tomono by almost 45 points, taking the gold medal overall by a 49-point margin.

[36] At the 2020–21 Japan Championships, Kagiyama placed second in the short program behind Yuzuru Hanyu and ahead of Shoma Uno, who fell on his attempted jump combination.

Kagiyama's father and coach, Masakazu, had recovered from the effects of his intracerebral hemorrhage in June 2018 that had prevented him from accompanying his son to international competitions since, and was able to travel to watch him compete in Stockholm.

[39] Kagiyama scored a personal best of 100.96 in the short program, landing two clean quads and a triple Axel to place behind Hanyu and in front of Nathan Chen.

[41] Kagiyama's placement combined with Hanyu's bronze medal position qualified three berths for Japanese men at the 2022 Winter Olympics.

[43] While practicing the quad Lutz in late August, Kagiyama suffered a bone contusion on his right hand that required a cast to be worn for two weeks.

He skated an almost clean short program, with the only mistake being a doubled planned triple toe loop on the back of his combination, and took the lead.

Kagiyama's first Grand Prix assignment was scheduled to be the 2021 Cup of China, but following its cancellation, he was reassigned to the 2021 Gran Premio d'Italia in Turin.

[48] Considered the pre-event favourite, he performed poorly in the short program, placing seventh of twelve after multiple jump errors.

[49] Kagiyama mounted a comeback in the free skate, his only error being a turnout on his opening quad Salchow attempt, winning that segment and the gold medal.

[50] At this second event, the 2021 Internationaux de France in Grenoble, Kagiyama won both segments of the competition to take his second Grand Prix gold of the season and defeat silver medalist and domestic rival Shun Sato by 21.42 points.

[51] Despite this convincing win, he said afterward that there was "much more regret than happiness" with regard to the second "disastrous" second half of his free skate, which featured three jump errors, including a singled attempt at a triple Axel.

With both Chen and Hanyu absent due to injury, Olympic medalists Shoma Uno and Kagiyama were rated as top contenders for the gold medal.

[63] In spite of this, he announced in early December that he intended to compete at the 2022–23 Japan Figure Skating Championships, against his father's advice to withdraw and prioritize recovery.

[67][68] Making his return to international competition in early September, Kagiyama won the gold medal at the 2023 CS Lombardia Trophy.

He was second in the free skate after a fall on a triple Axel, placing second after countryman Shoma Uno with 182.88 points, but managed to win the gold overall and qualified for the Grand Prix Final with an accumulated score of 288.39.

[78] Kagiyama competed at the 2024 Four Continents Championships in Shanghai in early February where he scored 106.82 points to win the short program.

[80] At the 2024 World Championships in Montreal, Kagiyama came narrowly second in the short program, 1.37 points behind segment leader Uno and just ahead of Malinin in third.

In the free skate, his only error came with a fall on a triple Axel, and he came narrowly third in the segment, but had the second-highest program component marks behind American Jason Brown.

[69] Going on to compete on the 2024–25 Grand Prix circuit, Kagiyama won gold at the 2024 NHK Trophy, over thirty-five points ahead of silver medalist, Daniel Grassl.

[84] One week later, Kagiyama would compete at the 2024 Finlandia Trophy, where he would win the short program but only place fifth in the free skate following several uncharacteristic jump errors.

[86] At the Final, Kagiyama placed second in the short program, almost twelve points behind Ilia Malinin, after unexpectedly falling on an attempted quadruple salchow.

[87][88] In late December, Kagiyama won the 2024-25 Japan Championships for the first time after winning both the short and free program segments.

[93] Kagiyama has contracts with multiple partners and most notably has an affiliate sponsorship agreement with Japanese foods and beverage company Oriental Bio that was announced in late October 2021.