Mikhail Grabskii was born in 1923 in Kiev. His father was a worker. After the German attack on the Soviet Union in June 1941, Grabskii volunteered for the Red Army. He took part in the battle of Stalingrad and was injured. After being released from hospital, he was sent to a tank course. During the Soviet offensive at the Dnieper River in the fall 1943, he was turret gunner of a T-34 tank.
In November 1943, during the operation for the liberation of Kiev, Grabskii's tank was among those ordered to take the town of Fastov, the site of a railway junction 65 kilometers (40 miles) southwest of Kiev. After several hour of skirmishes, the tank unit broke into Fastov. Grabskii's tank was the first to attack the German tanks in the town. The effect of this breakthrough was that the enemy retreated in panic, abandoning fifty loaded ammunition trucks and other materiel. However, after having assessed the size of the Soviet unit, they attempted to counter-attack with a greater number of tanks. The battle continued for twelve hours, during which Grabskii succeeded in destroying three German tanks. During that time, the main Soviet forces entered the town and the battle was over. Some of the participants of the breakthrough, including Grabskii, were awarded the title of Hero of the Soviet Union.
After the war, Grabskii settled in Kiev.
In 1982, Grabskii emigrated to the USA, where his son had settled. Grabskii lived in Florida. The Soviet authorities considered his emigration to be treason and deprived him of the title of Hero of the Soviet Union, together with his other military awards. In 2000, an appeals commission of the Russian Federation's Supreme Court restored his title and awards.
Mikhail Grabskii died in 2007 in St. Louis.