N.M. Stat. § 42-10-11
When homestead exemption does not apply.
The provisions of this article [42-10-9 to 42-10-12 NMSA 1978] do not apply or
extend to taxes, garnishment, recorded liens of mortgagees or lessors or recorded liens
of laborers or materialmen for labor or materials furnished for the construction or repair
of the dwelling house.