Makhmud was born in Starye Atagi, USSR to a Chechen family. When he was a child, his father would take him to village weddings where he would perform dances. At the age of fifteen, Makhmud joined the Checheno-Ingush Song and Dance Company, and at nineteen, he joined the operetta theater of Pyatigorsk, where he would give concerts to Red Army troops fighting in World War II.
In 1944, he was deported along with other Chechen people during the Deportation of the Chechens and Ingush, an ethnic cleansing of Chechen and Ingush people by the Soviet forces.
Makhmud was known for always wearing his papakha hat, calling it "my crown" and not even removing it when meeting with a head of state. His papakha made an unparalleled and very conspicuous presence on the floor of the Soviet legislature. On noticing it, the Soviet leaderLeonid Brezhnev would murmur that "Makhmud is here, it's time to call the session open."[3]