The attack happened Saturday afternoon in Tornillo while the woman, whose name was not reported, was visiting her grandson, the El Paso (Texas) Times reported.
The grandson's female pit bull attacked the 70-year-old, biting off her thumb, said El Paso County sheriff's spokeswoman Deputy Angelica Becerra.
When deputies arrived at the scene, the dog was showing signs of aggressiveness and was shot and killed by a deputy, Becerra said.
The woman was taken to a local hospital where doctors said they would try to reattach her thumb, Becerra said.
Notable deaths of 2014 [PHOTOS]