[1] He is the son of Ilona Melnichenko and Artem Torgashev, who competed for the Soviet Union in ice dance and pair skating respectively.

[3] Later in his career as a competitive figure skater, Torgashev also began working as a coach at the Great Park Ice & FivePoint Arena in Irvine, California.

Competing for in the ISU Junior Grand Prix series, he placed fourth in Ostrava, Czech Republic, and fifth in Tallinn, Estonia.

[8] Competing in the 2016 Junior Grand Prix series, he won silver in Russia and placed fourth in Germany.

During the 2017 Junior Grand Prix series, he won silver in Belarus with a personal best total score of 212.71 points and then placed fourth in Italy.

In September, he won gold at JGP Lithuania in Kaunas after placing second in the short program and first in the free skate.

[14] He struggled in the free skate, falling twice and stepping out of an under-rotated attempted quadruple toe loop in the program's second half.

[15] Assigned to the 2020 World Junior Championships, Torgashev placed third in the short program, winning a small bronze medal.

[17] In November 2019, Torgashev announced a coaching change as he moved from Colorado to California to train with Rafael Arutyunyan at Great Park Ice in Irvine.

[18] He was unable to compete during the 2019–20 and 2020–21 figure skating seasons due to an injury in his right foot that ultimately required ankle surgery as well as a long rehabilitation.

[20] He placed fifth in the short program, and then won the free skate, winning the overall bronze medal with a total score of 255.56 points.

He was provisionally selected for the 2023 World Championships in Saitama, Japan, pending his acquisition of the requisite scores at the International Challenge Cup.

[29] At the NHK Trophy, Torgashev delivered a strong short program, earning a new season's best score, finishing fourth in that competition segment.

[30] Following his success on the Grand Prix series, Torgashev expressed elation, saying, "I packed for a few days trip to France, and ended up staying for a while more week in Japan.