Born in Stepanovka, a village in what was Kherson Governorate,[1] Kuznetsov was the son of a wealthy landowner and began school in Odessa, where his artistic talent was discovered and he began taking lessons at the local drawing school.

At this time, he successfully defied his family's wishes and married a working-class woman who was employed there.

After an accident in 1889, he had to walk on crutches, so he worked entirely in a studio at his estate, which became a meeting place for the creative community, including figures such as Fyodor Chaliapin, in addition to artists.

Two years later, he was offered a professorship at the Imperial Academy, where he taught battle painting, but left in 1897 to return to Odessa.

In 1920, during the Russian Civil War, as the White Army retreated, he and his family emigrated to Yugoslavia, eventually settling in Sarajevo, where he died in 1929.