Mandy Peynado's arms were savaged as she tried to protect her throat when the dog attacked her at Knightwood Kennels near Salisbury, Wiltshire.
Claire Gourley, Mandy's sister, said: "Her spirits are fairly good and the doctors are saying she is a miracle."
Ms Peynado, 47, is due to go back into theatre on Monday for more surgery.
During Saturday's operation, surgeons took muscle from her back and used it as a skin graft to preserve her right arm.
Dog destroyed
Doctors are still unsure whether they can save what remains of the top of left arm.
Ms Peynado had worked at the kennels for three years before the attack.
The dog had been picked up as a stray by New Forest District Council six weeks earlier and had not shown any signs of aggression.
The kennel's owner Judith Wykeham said it would have been treated differently is she had known it had a troubled background.
"Apparently there was a history with the owner who abandoned the dog and the police are investigating," she said.