Dobrokovsky studied at the Higher State Artistic and Technical Workshops (VKhUTEMAS) in Moscow (1923–1924) and in early 1930s — at Leningrad Institute of Proletarian Visual Arts (INPII).

Dobrokovsky was a member of the Society of Easel Artists (OST, 1925–1927), participated in the 1st and the 3rd exhibitions of this society. He was the founder member of the association Oktyabr (“October”, 1928–1930).

Dobrokovsky designed and illustrated books Scarlet oil by A. Kosterin (1923, Molodaya Gvardia publishing house), Miracle Fish by N. I. Komkolov (1928), Forest Lake by N. P. Plavilshikov (1929) and etc.

He also designed covers for the magazines Dayesh (“Let there be”, No. 3, 1929) and Brigada Khudozhnikov (“Brigade of Artists”, No. 5/6, 1931).

Since 1923 Dobrokovsky collaborated with the magazine Bezbozhnik u Stanka (“Atheist at the Machine”), where he worked with A. Deineka, D. Moor and M. Cheremnykh. After becoming friends with D. Moor and under his influence, Dobrokovsky became engaged in poster art. He created posters: Kaveh the blacksmith (1921), Song of the collective (1928) and We are going full steam ahead on the path from industrialization to Socialism (1931). In 1925 Dobrokovsky was awarded a gold medal and a diploma at the International exhibition of fine and decorative arts in Paris. In early 1930s he joined the Association of Book and Poster.

Dobrokovsky participated in exhibitions: the First state travelling exhibition of paintings (1925, Moscow, Saratov, Stalingrad, Novgorod, Kazan), the International exhibition of fine and decorative arts (1925, Paris), the First exhibition of graphic art (1926, Moscow), the International exhibition Art of the Book (1927, Leipzig, Nurnberg), the Exhibition of acquisitions of state commission of acquisitions of works of fine art (1928, Moscow), Modern book art at the international exhibition of press (1928, Cologne), Exhibitions of the Russian Art (1929, Winterthur, Switzerland), the second travelling exhibition (1930, Novgorod, Kazan, Sverdlovsk, Perm, Ufa, Samara, Saratov, Penza etc), the First exhibition of the group Oktyabr (“October”, 1930, Moscow), the Exhibition of the graphic art, drawing, poster and book (1930, Danzig), the exhibition Poster in the service of five-year plan (1932, Moscow), the exhibition Caricature in the service of the socialist formation (1932, Moscow) and others.

In early 1930s Dobrokovsky worked at the newspaper of one of the sections of the Communist International (Comintern), later at the newspaper Rulon (“The Roll”), at the wall newspaper of Ryazan tram depot and at the wall newspaper of faculty of philosophy at Moscow State University. He also worked on design of the Persian room of the Institute of Oriental Studies.

On the instructions of the newspaper Izvestia, Dobrokovsky worked as an artist on Kandopozhskaya wood-pulp factory in 1932. There he designed posters, drew caricatures, designed performances of the brigade.

In mid 1930s Dobrokovsky cooperated with the magazine Krokodil (“Crocodile”). At the same time he painted a series of landscapes of the city Kasimov.

In 1938 he was accused of espionage for the Polish counter-revolutionary espionage and terrorist organization. Dobrokovsky was shot at the Butovo firing ground. He was rehabilitated in October 1957.

Works by Mechislav Dobrokovsky are in many museum collections, including the State Tretyakov Gallery, and in private collections.