A witness said Margaret Salcedo, 48, of Truth or Consequences, tried to use her cell phone as the attack began but a dog bit her arm and she dropped the phone.
The dogs bit Salcedo all over her body, Laura Russell told KOB-TV, Albuquerque.
Authorities said they believed the attack lasted about three minutes.
An officer responding to a 911 call by Russell shot one dog when it charged him, while the other dogs ran off.
Salcedo was conscious at the scene but later died, police said.
Police said they think the dogs got loose from a home nearby and the district attorney would decide whether to file charges against the owners.
"I think it's like living in the Middle Ages where you hate to go outside because the wolves are going to eat your grandchildren," resident Elizabeth Stout told KOB-TV.