Born into the family of a first-guild merchant from Kungur, Grigory Kirillovich Kuznetsov. He studied at the Petersburg Commercial School but did not complete the full course. Due to health issues, he spent most of his life at his estate in Foros in Crimea and in Nice in southern France.

In 1883, he inherited a multi-million fortune from his maternal grandfather, A. S. Gubkin, a Kungur merchant who donated over 1.5 million rubles for the establishment of a Technical School and the Elizabethan Home for the Care of Poor Children in Kungur, which later became the Elizabethan Handicraft School. Continuing his grandfather's work, A. G. Kuznetsov annually allocated hundreds of thousands of rubles for the maintenance of these educational institutions, built a summer house for the students of the handicraft school in the city’s pine forest, and the Nikolsky Church over his grandfather's grave.

Kuznetsov also made significant contributions to the development of the Yalta progymnasium, public schools, and hospitals in the Moscow province, donating large sums to the Orthodox community in Warsaw to support the church. In 1892, a book titled "Tea and Tea Trade in Russia and Other States" was published at his expense.

His donations led to the establishment of Russian biological stations in Sevastopol and Villafranca. Thanks to Kuznetsov, ancient acts of Vyatka and Kungur, works of Herodotus, Thucydides, Polybius (translated by F. Mishchenko), Titus Livius (translated by Adrianov), studies by Professor Kulagin, and an album of photogravures with paintings by V. E. Makovsky were published. He also facilitated the publication in French of the works from the Moscow International Congress of Naturalists in 1892.

Having become the owner of Foros, Kuznetsov transformed it into a model estate of European type. He created the famous Foros Park, now a monument of garden and park architecture, and built a palace ensemble that has survived to this day. The interiors of the main palace, designed in the classical style, were decorated by Y. Y. Klever, Chagin, and Makovsky. In 1892, on the Red Rock above Foros, the Church of the Resurrection of Christ was built in Byzantine style, designed by architect Nikolai Chagin, in honor of the salvation of the royal family near Borki, becoming one of the attractions of the southern coast of Crimea.

Kuznetsov's famous yacht, one of the most beautiful and largest private yachts, was named "Foros." In 1894, English King Edward VII was a guest on it in Cannes.

Kuznetsov passed away at his estate in Ostashevo near Moscow and was buried in the family crypt at the Novoe-Alekseevsky Monastery cemetery in Moscow.