N.M. Stat. § 39-4-9
All the executions taken out of district courts shall be returned within sixty days from the date of the delivery thereof, to the sheriff or other officer, or person whose duty it is or who may be designated to serve the same; and such sheriff, or other officer or person, may offer for sale, and sell at public auction, at such time and place as may be designated, any real estate taken by virtue of such execution, complying with the provisions of the law, providing for appraisements, and by giving twenty days public notice of the time and place of the sale, in the manner provided by law. All personal property, taken by virtue of any execution, may be sold as provided by law. All executions may issue on application, and the service and return thereof shall be controlled by the plaintiff or his agent.
NMS § 39-4-9