N.M. Stat. § 38-1-15
For the purpose of the preceding section [38-1-14 NMSA 1978], it is considered that an action is pending from the time of filing such notice; provided, that such notice shall be of no value, unless it is followed by the service of such citations or process of citation, or by notice by publication to the defendant, as provided by law, within sixty days after such filing. And the court in which said action was commenced, may in its discretion, at any time after the action shall be settled, discontinue or revoke on application of any person injured, and for good cause shown, and under such notice as may be directed or approved by the court, order the notice authorized by the preceding section to be canceled by the county clerk of any county in whose office the same may have been filed, and such cancellation shall be made by an indorsement to that effect upon the filed notice which shall refer to the order.
NMS § 38-1-15