Khanmammadov was born in Derbent (present-day Dagestan, Russia) and began studying tar at age 10.

In 1932, the boy's life experienced a major change when his father and uncle were arrested during the Great Purge and permanently exiled to Siberia on account of owning land.

After Khanmammadov graduated from middle school, his mother, who was struggling to take care of six children, sent him to Baku to find Uzeyir Hajibeyov, an Azerbaijani composer known for his patronage of the arts.

In 1946 he was sent to Tabriz, then ruled by the Soviet-backed Azerbaijan People's Government to found a philharmonic orchestra but after the Soviets' withdrawal returned to Baku.

Khanmammadov also wrote two successful musical comedies: Bir dagiga ("One Minute", 1961; lyrics by Maharram Alizadeh) about the life of oil workers; and Butun arlar yakhshidir ("All Husbands Are Good", 1971; lyrics by Alexander Khaldeyev in Russian).