New Mexico doesn't have a specific auto-renewal law, but the UPA (no specific auto-renewal law) (N.M. Stat. § 57-12-2) plus federal FTC rules protect your right to cancel.
N.M. Stat. § 57-12-2
Penalties: Actual damages plus civil penalties up to $5,000
SubScrub automatically cites N.M. Stat. § 57-12-2 and federal laws