The feisty wife of a world-renowned Russian sculptor emasculated an armed thug outside her Soho home — saying he “didn’t have the cojones to shoot her,” police sources said yesterday.

Fearless Anna Graham, 54, was smoking a cigarette near her unlocked car, which she was loading for a trip, when the muggers approached her at about 1 a.m. on July 3.

One bandit pulled out a pistol, cocked it, and pressed it against Graham’s head while demanding her wallet.

But the slim brunette coolly replied that she didn’t have one, then told him he “didn’t have the cojones to shoot her,” the sources said.

The accomplice, who was rifling through the car, repeatedly urged his buddy to shoot Graham, who was described as “strong-willed” and “self-assured” in a 2002 biography of her husband, Ernst Neizvestny.

The crooks were interrupted by a female friend of Graham’s who came out of the ground-floor apartment at 81 Grand St. that doubles as Neizvestny’s studio.

That woman tried to stop the man who was ransacking the car, but he kicked her and knocked her to the ground, cops said.

When another friend came outside, both thieves demanded her purse, then ran off when she said that she didn’t have one, police said.

They were last seen fleeing north on Greene Street.

Graham’s daughter, Olivia, 24, admitted her mom “definitely has a mouth on her.”

“I guess I’m pretty impressed with the way it worked out,” she said.

The couple’s dog-walker said she didn’t think that taunting the mugger was necessarily “a stupid thing.”

“I think she can read people,” the woman said as she took the couple’s bulldog and Italian mastiff for a stroll.

A neighbor described Graham as a tough cookie. “She doesn’t take s–t from anyone,” said Angus Kneale.

According to “Centaur: The Life and Art of Ernst Neizvestny,” Graham, who formerly worked as a translator and interpreter, “was a cultured, refined Russian emigré who immediately caught Neizvetstny’s eye when they first met.”Neizvestny, 88, was the leading memorial builder of the Soviet era and has been called the world’s greatest living Russian sculptor.

He was infamously derided by then-Soviet Premier Nikita Khruschev, who likened Neizvestny’s art to what one would see if seated inside a toilet.

But Neizvestny got the last laugh when he was later commissioned to create a memorial for Khrushchev’s grave.

Additional reporting by Jamie Schram, Larry Celona, Kevin Fasick and Jennifer Bain