Mexico has never had the worlds greatest navy, so I'm going to assume you're going back all the way to the Spanish Armada. I'm not aware that any profound deforestation of Mexico was done to provide timbers for the Armada.

Now when I lived in Belize, I learned that timbers were a major colonial resource that was extracted by the British, first for logwood (used for red dye), and later for mahogany. The Spanish also extracted logwood, including from Mexico on the Yucutan peninsula. As far as I know, most colonial deforestation in Mexico occurred more for local building materials, fuel, and to clear land for agriculture than for anything else. Apparently the areas where silver mining was taking place were especially stripped barren of natural resources.