The SSPCA is appealing for information after the animal, called Buttons, was found seriously injured at Vale of Leven Golf Club.
She was returned to her owner, in Alexandria, with a wire snare around her abdomen and another around one of her back legs.
Her owner took her to a vet, who had to amputate the leg.
SSPCA Chief Superintendent Mike Flynn said: "A member of the public discovered Buttons with the snares caught around her.
"Unfortunately, she ran away before anyone was able to help her.
"It's remarkable that Buttons made it home.
"The snares were both illegally set and we are very keen to identify the person responsible.
"Vale of Leven Golf Club have confirmed that no-one is authorised to set snares in their grounds."