N.M. Stat. § 73-1-16
The directors elected pursuant to such election code shall be elected for a term of six years each. Each director shall hold office for the term for which he was elected, and until his successor is duly appointed, or elected, and has qualified, except as hereinafter provided, being removable therefrom only for cause after a hearing upon a motion filed by any interested person in the original proceeding in which the district was organized. Unless otherwise provided by the election code, vacancies shall be filled by appointment of the district court having jurisdiction. Upon the election of the first board of directors, the directors shall draw numbers by lot; numbers one (1) and two (2) shall serve two (2) years; numbers three (3) and four (4) shall serve four (4) years, and number five (5) six (6) years.
NMS § 73-1-16