Stay out of the big cities. Small town living is easy in Mexico, and it's the best way to live off the grid. Areas surrounding Guanajuato, Queretaro and Morelia are especially well-known for conserving the colonial lifestyle and being devoid of tourists and foreign intrusion in general. Once you reach the main cities in those areas, simply hire a driver or rent a car and drive a few hours in any direction to find remote towns and villages.
Use your foreign status to find off-the-books work. As soon as you start paying taxes, you will be easy to locate and track. If you truly want to live undetected, you can try teaching English at small private schools or to exchange private tutoring for food and shelter. You can also look for a job as a babysitter or nanny, or join other expats who are traveling their way through Mexico by either teaching or volunteering.
Buy or build your own home, focusing on making the most of the environment so you can eliminate the need for utilities. For example, living in the desert, near the United States border crossing and the Sonoran and Chihuahuan Desert areas, will eliminate your need for heating, while staying near rivers or the ocean will make it easier to live without running water.
Take advantage of the weather to set up solar energy panels. Mexico is well-known for its clear skies and sunny weather all year long, especially if you head outside of the cities and inland, away from the more humid coastal areas. If you want to stay near the water, the coast of Nayarit is remote enough to allow you to mix in with the local population. Otherwise, head to the central plateau for better weather and more privacy.
Learn to live from the land. Lots of people in Mexico, especially in impoverished areas, grow their own gardens or raise cows for milk. Even if you're not ready to start your own farm, you can choose one area (such as gardening or crops) and then barter with your neighbors for the products they have. This is an especially good idea in rural areas, where access to shops is limited.