Mitta's birth name was Alexander Naumovich Rabinovich (Russian: Рабино́вич). He studied engineering (graduated in 1955), then worked as a cartoonist in art and humour magazines. In 1960 Mitta graduated at the film directing faculty of the VGIK.
Mitta's career as film director and screenwriter spans from the 1960s until the 2010s. Among the movies are Shine, Shine, My Star (1970) about actors trying to survive and work during the time of the Russian revolution or the high budget catastrophe movie Air Crew (1979). For his work Mitta obtained numerous awards in the Soviet Union and Russia.
- 1961: My Friend, Kolka!
- 1962: No Fear, No Blame
- 1965: They're Calling, Open the Door
- 1969: Shine, Shine, My Star
- 1972: Dot, Dot, Comma...
- 1974: Moscow, My Love
- 1976: How Czar Peter the Great Married Off His Moor
- 1979: Air Crew
- 1982: The Story of Voyages
- 1988: A Step
- 1991: Lost in Siberia
- 2000: The Border. Taiga Romance
- 2002: Red-hot Saturday
- 2004: Swan Paradise
- 2013: Chagall — Malevich
In the 2000s Mitta began a film school.
- "Berlinale 1980: Juries". berlinale.de. Retrieved 2010-08-15.
- Грачёв, Сергей (26 August 2014). "Александр Митта: «Россия нищает, а все делают вид, что так и надо»". www.aif.ru. Retrieved 1 May 2018.