If any dog shall kill or injure any livestock, the owner or keeper of such dog shall be liable for all damages that may be sustained thereby, to be recovered by the party so injured before any court having competent jurisdiction, and it shall be unlawful to keep such dog after it is known that the dog is liable to kill livestock, and it shall be the duty of the owner to kill, or have killed, the dog upon order of the court after a finding that the dog has killed or injured livestock, and provided further, that it shall be the right of any owner of livestock so killed or injured by the actions of any dog to kill the dog while it is upon property controlled by the owner of the livestock.
NMS § 77-1-2