Khutsiev's father, Martyn Levanovich Khutsishvili (the family's original Georgian surname), was a lifelong Communist who was purged by Joseph Stalin in 1937. His mother, Nina Mikhailovna Utenelishvili, was an actress. Khutsiev studied film in the directing department at the Gerasimov Institute of Cinematography, graduating in 1952. He worked as a director at the Odessa film studio from 1952 to 1958, and worked full-time as a director at Mosfilm from 1965 onwards.
Khutsiev's first feature film, Spring on Zarechnaya Street (1956), encapsulated the mood of the Khrushchev Thaw and went on to became one of the top box-office draws of the 1950s. Three years later, Khutsiev launched Vasily Shukshin "as a new kind of popular hero" by starring him in Two Fyodors.[1] His two masterpieces of the 1960s, however, were panned by the authorities, forcing Khutsiev into something of an artistic silence. Since 1978, Khutsiev has taught film directing master classes at the VGIK.
His 1991 film Infinitas won the Alfred Bauer Prize at the 42nd Berlin International Film Festival.