N.M. Stat. § 39-6-4
Any livestock taken under any process, as provided in the foregoing section [sections] [39-6-1 to 39-6-3 NMSA 1978], shall be disposed of by the sheriff, or officer, as provided by law: provided, that in the case of a levy of a writ of execution, under the three preceding sections [39-6-1 to 39-6-3 NMSA 1978], the officer shall forthwith proceed to sell any livestock so levied upon, as now provided by law, in lots, from time to time as he may come into possession of the same, until the writ is satisfied. And upon such writ being satisfied he shall at once enter satisfaction thereof, in all cases, upon the margin of the record aforesaid, where such brand is recorded, and shall indorse [endorse] such satisfaction upon all process filed as aforesaid.
NMS § 39-6-4