N.M. Stat. § 7-1-47
Any person whose property has been levied upon shall have the right to pay the amount due, together with the expenses of the proceeding, or furnish acceptable security for the payment thereof according to the provisions of Section 7-1-54 NMSA 1978 to the department at any time prior to the sale thereof, and upon payment or furnishing of security, the secretary or the secretary's delegate shall restore the property to that person, and all further proceedings in connection with the levy on the property shall cease from the time of the payment. Any person who has a sufficient interest in property or rights to property levied upon to entitle the person to redeem it from sale, according to the provisions of this section, who does pay the amount due and accomplishes the redemption shall have a lien against the property in the amount paid and may file a notice thereof in the records of any county in the state in which the property is located and may foreclose the lien as provided by law.
NMS § 7-1-47