Botev, the oldest club in the country, handed the reins to the former Levski Sofia boss after having sacked Nikolay Kostov last week.
Several dozen hostile supporters invaded the team's training ground in Komatevo shortly after the start of Mitov's first session, shouting: "You're not welcome here. You should leave immediately".
Botev 'ultras', the club's hardcore fans, also threatened the coach with physical abuse as they believe he is still a supporter of bitter rivals Levski.
The 44-year-old won the league title with Levski as a player.
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Mitov and his assistant, former Bulgaria international Marian Hristov, stopped the session and the new coach then announced he was leaving.
Just two hours earlier Mitov had told a news conference he felt "very happy" and "honoured to lead such a big and beloved team".
Angered by the reaction of the fans, Botev owner Rumen Chandurov also decided to resign.
"I don't know what to say, disrespect, disrespect, disrespect," he told local media. "They forced me to quit."
Twice champions Botev have started the season with two wins, two defeats and one draw.
(Editing by Tony Jimenez)
