N.M. Stat. § 3-14-10
At the first meeting of the new commission after each election, or as soon thereafter as practical, the commissioners shall select one of their number as mayor to act for two years, or until a successor is selected and qualified, unless sooner removed by death, resignation or removal from office. The mayor shall preside at all meetings of the commission and perform other duties, consistent with his office, as imposed by the commission. The mayor has all powers and duties of a commissioner, including the right to vote upon all questions considered by the commission. He is the official head of the municipality for all ceremonial purposes, for the purpose of civil process and for military purposes. During his absence or disability, his duties shall be performed by another member of the commission, appointed by a majority of the commission and designated as mayor pro tem.
NMS § 3-14-10