Alexander Vyazemsky was born on August 3 (14), 1727, and came from a princely family, tracing its roots to the grandson of Vladimir Monomakh, Prince Rostislav Mstislavich. At the age of twenty, he graduated from the Land Noble Corps. During the Seven Years' War with Prussia, he not only participated in battles but also carried out secret missions for the command, which nearly cost him his life. By the end of the war, Vyazemsky held the position of General Quartermaster and was known to Empress Catherine II. In December 1762, she tasked him with regulating relations between peasants and their landlords at the Ural factories. He worked on this task for almost a year until he was replaced in December 1763 by Major General A. I. Bibikov.

On February 3 (14), 1764, Catherine II, having confirmed Vyazemsky's honesty, appointed him Attorney General of the Senate and personally wrote him a "top-secret instruction" outlining his duties. The Empress reminded him that the Attorney General must be candid with the sovereign, as his task was to oppose the powerful of this world, and only imperial authority could assist him in this. She emphasized that she did not require "flattery," but only honesty and firmness in matters. Catherine II warned him against court intrigues and advised him to be guided solely by the benefit of the homeland and justice.

Vyazemsky strictly followed the instruction and enjoyed the trust of the Empress, which allowed him to hold the position for nearly 29 years and expand his powers. Early in his career, he headed the Senate and controlled the sale of salt and wine, and from the 1780s, he managed justice, finance, and internal affairs. He introduced strict accounting in financial matters and oversight of income and expenses.

The Attorney General led the Secret Expedition, through which all significant political cases of the Catherine II era passed, including the cases of E. Pugachev, A. N. Radishchev, and N. I. Novikov. During his tenure, S. I. Sheshkovsky, known as the "domestic executioner of gentle Catherine," was active.

Vyazemsky actively supervised prosecutors and introduced the "Institutions for the Administration of Provinces" in 1775, regulating the rights and duties of local prosecutors. For his merits, he received numerous awards, including the Orders of St. Andrew the First-Called, St. Alexander Nevsky, St. Anna, and others. He held the rank of General Lieutenant and Actual Privy Councillor.

In September 1792, Vyazemsky retired due to illness, and his duties were distributed among several individuals. D. N. Bantysh-Kamensky wrote of him as a loyal servant to the throne, a selfless and hardworking man who knew how to choose worthy assistants but was stingy and envious.

Prince Vyazemsky died of paralysis on January 9 (20), 1793, and his grave is located in the Annunciation Church of the Alexander Nevsky Lavra. His estate, Murzinka, was inherited by his daughter Anna, and then by her grandson Anton Apraksin.