The University Libraries home page - database section - offers several sources for newspaper articles online, both historical and contemporary. To use them you need a UNM login or to be working at a UNM Library computer.
The databases are grouped under Alpha letters.
Under Alpha N - Newspapers - Newspaperarchive - Accessnewspaperarchiveonline - you can limit for New Mexico newspapers - has scanned news pages for Santa Fe from 1849-2015 and Albuquerque and Las Vegas from 1880-1977. There are some newspapers from more recent decades for other New Mexico communities. (Access Newspaper Archive Online can also search newspapers in other states and some countries).
Alpha C - Chronicling America (Library of Congress website) - has scans of New Mexico Spanish language newspapers before 1922. (It also can search early newspapers in other states).
Alpha N - New Mexico Newspapers - has online news articles for Albuquerque since 1995 and Las Cruces and Roswell since 2004.
Tip: Also see another useful related libguide about newspapers for this area and beyond.
Besides on Chronicling America, the New Mexico newspapers dating before 1922 are also available for reading online and with easier access on UNM Digital Repository.