In the Hunger Games , when Cato was overpowered by the mutts, it took hours before Katniss shot him. However, if she didn't do that, then will the mutts eventually kill him or spare him?
Probably not directly, but he would eventually die of his wounds.
After spending an entire night on top of the cornucopia while Cato is being mauled by the mutts, we see this exchange:
"Why don't they just kill him?" I ask Peeta.
"You know why," he says, and pulls me closer to him.
Hunger Games, p. 339
Clearly, the gamemakers are trying to draw this out as long as possible, probably hoping to get Katniss to kill both Cato and Peeta. However, they will also not send in medical help except to the Victor, so while the Mutts will definitely not go in for the kill and finish him, Cato would eventually die, probably as a direct result of wounds from the Mutts.