He lived as an émigré in the Tsardom of Russia and subsequently served as first General of the Artillery (Feldzeugmeister), the second highest military rank under Tsar Peter the Great.

Alexander was born in Tbilisi to Archil, a Georgian prince of the Mukhranian Bagrationi royal line and sometime King of Imereti who subsequently fled the anarchy in his country to the Russian Empire.

On 30 July 1688, Alexander and Mamuka left Moscow to join their father in his eventually failed attempt to recover the lost throne of Imereti.

On 19 May 1700 he became the first Russian officer to be promoted to the rank of General Feldzeugmeister and appointed the chief of the Pushkarsky Prikaz (literally, "cannon administration").

[2] With the outbreak of the Great Northern War, in which Russia confronted Sweden, Prince Alexander was put in command of the Russian artillery.

In the ensuing battle of Narva, a relief army led by Charles XII of Sweden inflicted a disastrous defeat on the Russian forces on 19 November 1700.

[4] According to Voltaire's 1731 Histoire de Charles XII, the captured Prince Alexander was snatched by the Swedish general Count Carl Gustav Rehnskiöld from the hands of Finnish soldiers who were about to kill him.

In 1708, the prince and other Russian detainees were discovered to possess drawings of Swedish fortifications, and on Charles XII's order, their rights, including that of correspondence, were again restricted.

Alexander, however, continued to enjoy certain favor with the dowager queen and Princess Ulrika Eleneora and was allowed, to the displeasure of the Defense Commission, to visit the court.

The marriage produced Alexander's only child, Sophia (18 September 1691 – 4 January 1747), who married Georgian exile in Russia, Major-General Prince Igor Dadiani (1691–1765).