Mordvinov's early work, prior to his graduation from Moscow State Technical University (MVTU) in 1930, is definitely Constructivist, best seen in his Kharkiv Post Office of the late 1920s.

In 1929-1932, Mordvinov, Karo Halabyan and Alexander Vlasov were the founding members of VOPRA, a group of young 'Proletarian Architects' who attacked proponents of the Constructivist movement, notably Ivan Leonidov, and all other "alien art" like eclectics, formalism and even baroque: "There is no class-free art, neither class-free architecture" ("Бесклассового искусства у нас нет и бесклассовой архитектуры тоже нет" - Khan-Magomedov cites Mordvinov's March, 1928 speech).

Formation of Union of Soviet Architects in 1932 allowed Mordvinov to move from small-time criticism to an executive position; he acquired bureaucratic muscle and set up his own workshop, present in all architectural contests of the 1930s.

His influence was reinforced by a 1947 commission to design one of the Moscow Skyscrapers, now known as the Hotel Ukraina, which he shared with Vyacheslav Oltarzhevsky, one of the few Soviet experts in highrise construction.

In 1956-1964, Mordvinov completed two major projects - redevelopment of Komsomolsky Prospekt and greenfield Cheryomushki District which became the symbol of Khrushchev's affordable housing initiative.