Does Mexico defend its border?

Yes it does. The Mexican Armed Forces (Fuerzas Armadas de Mexico) are composed of the Mexican Army which includes the Mexican Air Force (FAM) as a subordinate entity and the Mexican Navy which also includes the Mexican Naval Infantry and Naval Aviation (FAN).

However it must be noted that Mexico has always adhered to the principles of non-interventionism. Therefore its military has a more passive stance than in most other countries. Besides, it has no "natural enemies" to defend from.