Career
Levski Sofia
Mitrev came through the youth ranks at Levski Sofia. Foreign 2006-2007 season he was promoted to the first squad as third choice behind Georgi Petkov and Nikolay Mihaylov. He made his debut in a 3–0 home loss against Werder Bremen in the group stage of the Champions League on 31 October 2006, replacing Nikolay Mihaylov at half-time.
On 5 December, Mitrev played in Levski"s 2–0 defeat to Chelsea at Stamford Bridge, making several excellent saves, including one reaction save from a Michael Essien header.
However, he received criticism from the Chelsea faithful for a bad challenge on Didier Drogba, clearly fouling him. Chelsea were not offered a penalty, however Drogba accepted the apologies of the goalkeeper.
On 10 March 2009, Mitrev scored 90-meters goal for the second team of Levski in a game against Vihren Sandanski. Mitrev finished the season with 7 appearances in the league, as Levski clinched the A Group.
Mitrev left Levski on 1 July 2012 after his contract with the club expired.
He spent six seasons of his career with Levski, mainly as a backup. He played 52 competitive games in all competitions. Lokomotiv Sofia
After six months without a club, Mitrev joined Lokomotiv Sofia on 28 December 2012.
He made his debut in a 2–0 away loss against Lokomotiv Plovdiv on 2 March 2013.
Mitrev left the team from the Nadezhda district after the 2014/2015 A PFG season when it was administratively relegated to the V group, as it was unable to obtain a license for professional football due to failing to meet the deadlines to pay for or provide sufficient guarantees regarding its debts. Sheriff Tiraspol
In June 2015, Mitrev moved abroad for the first time, joining Moldovan club Sheriff Tiraspol.
On 7 February 2015, Mitrev made his first appearance for Bulgaria, in the 0–0 draw with Romania in a non-official friendly match, playing the first 45 minutes. He earned his first cap on 8 June 2015, in the 0:4 loss against Turkey in another exhibition game, being between the sticks for the entire duration of the match.