N.M. Stat. § 19-7-35
That no lease of state lands for agricultural or grazing purposes shall be canceled or forfeited by the commissioner of public lands, before the expiration of the full term thereof, without the written consent of the lessee, except for fraud, collusion, mutual mistake or default of the lessee, and the right to cancel or forfeit such lease without cause, based on any agreement or consent contained in such lease is hereby waived. All sales of state lands embraced within such lease shall be made subject to all the terms and provisions thereof, except the right of the lessee to a renewal at the end of the term. Provided that nothing in this act [section] shall prevent the commissioner from granting right-of-way [rights-of-way] and easements over, across or upon the land embraced in the lease for public highways, railroads, tramways, telegraph, telephone and power lines, irrigation works, mining, logging and business leases.
NMS § 19-7-35