Shevtsov started his professional career at age 15, playing in the Ukrainian Second League for Krystal Kherson.

[8][9][10] In summer 2020, Shevtsov was on the first team of Desna Chernihiv, for their Europa League third qualifying round match against VfL Wolfsburg, appearing in the second half as a substitute.

[19] On 5 June, he made his league debut against Greenville Triumph, replacing Grayson Barber in the 63rd minute.

[24] On 6 September 2024, Shevtsov joined Ukrainian Premier League side Chornomorets Odesa,[25] making his debut against Obolon Kyiv on 4 October 2024.

[29] On 13 November 2020, he scored his first goal for the Ukraine under-21s in a 4–1 away victory over Malta, in a 2021 UEFA European Under-21 Championship qualifier.