Aleksandr Mardakhaiev was born in 1918 in Derbent, in Dagestan, in the far south of Russia, into a family of Mountain Jews. In 1924, his widowed father and the rest of the family moved to Makhachkala (the capital of Dagestan), where Aleksandr graduated from school – the same school where the future Hero of the Soviet Union (also a Mountain Jew) Shatiel Abramov was also studying. In 1938, Aleksandr was drafted into the Red Army and sent to a school that trained border guards. There he decided that army would be his vocation. He completed the course as a senior lieutenant.
With the beginning of the Soviet-German war, Mardakhaiev was sent to the front. In the fall of 1941, he took part in the defense of Moscow as a tank commander. In November 1941, during a tank battle, his tank successfully put two enemy anti-tank guns out of action and hit three enemy tanks. However, his tank was hit and caught fire. Acting like the famous Soviet military pilot Gastello (who aimed his burning aircraft at a column of enemy tanks and destroyed them), Mardakhaiev pointed his burning tank at the Germans. At the last moment he opened the hatch of his tank and, standing on it being enveloped in flames, he continued shooting at the enemy. This account of Mardakhaiev's death was confirmed by captured German soldiers.
Mardakhaiev was buried in a common grave in a village near Moscow.
Aleksandr Mardakhaiev was posthumously awarded the Order of Lenin. He was the first person from Dagestan to be given this award.