Mishchevskij was born in Mineralnye Vody (North Caucausus) on 1 July 1933. From 1953 to 1959, he studied voice at the Moscow
conservatory with Sergej Judin.
He made his debut the same year at the Stanislavskij and
Nemirovich-Danchenko Musical Theater, where he was to stay for his entire career.
His repertory of about 50 roles included: Lenskij, Vodemon, Rodolfo, Almaviva, Nemorino, des Grieux, ... He sang a lot on the
radio, as well.
In the evening of 25 January 1986, after having sung Lenskij, he was killed on his way home from the theater; the murderers were
never identified, and the case never solved.