Mitov joined Charlton Athletic in 2013 from Bulgarian club Chavdar Etropole.In April 2015, he scored a goal from his own six-yard box against Coventry City U18's, gaining press attention. He featured for the club at under-18, under-21 and under-23 level but did not make a senior appearance for the club. In February 2015, Mitov joined Canvey Island on a one-month loan. He made a single appearance in a 1–1 draw with Lewes on 28 February. Following his release from Charlton Athletic, Mitov joined Cambridge United on a two-year contract. On 16 May 2018, he extended his contract with until 2021. During the 18–19 season, Mitov became the first choice goalkeeper and made 21 league appearances in total over the season. He put in a remarkable performance in his team's 1–0 victory over Newcastle United on 8 January 2022 and was subsequently named the Cambridge Player of the Season in April 2022.