Yes, in general it is permitted for one to drive in the United States in a vehicle with foreign license plates, such as those that are Mexican tags. I see Mexican plated vehicles from time to time in my area.

While it is usually legal to drive in the US with foreign plated cars, state laws do differ so you should contact the Department of Motor Vehicles of the state or states which you want to drive in to see how long you are allowed to drive your vehicle with its Mexican license plates and what laws they have that may affect you, such as what car insurance coverage is required, do you just need a valid Mexican driver's license to operate in their state or get a US license after a certain time period, etc.

There are also certain documents that you likely will need to show at the border crossing to come into the United States and drive back to Mexico so check with the US customs and border patrol as well as the Mexican customs to see what they will require you show.