What happens if a soldier avoids a deployment by fleeing to Mexico?

I believe this could be called desertion and desertion can be punishable by death.

If Andrew Tahmooressi provided any example, Mexican authorities don’t take very kindly to Americans who they think are up to no good.

You need to tell your friend to quit being a nancy, grab onto his bootstraps, and remove his head from his 4th point of contact. The ramifications for what you're asking about are a lot worse than going to the box as a commo guy (assuming that's what your friend does too). Anyone who has signed up since September 11, 2001 shouldn't have signed up at all if they weren't prepared to deploy. It's no secret that we've been involved in numerous on-going armed conflicts around the globe for the last 16+ years.

Pretty sure the maximum punishment for desertion during war time is death by hanging or firing squad. I hear the cartel isnt fond of us military to begin with. He might find himself in a barrel of concrete.

Honestly what's most likely to happen is nothing. Desertion isn't prosecuted like it used to be, and he will probably get a dishonorable or an OTH discharge and that'll be it.

Desertion; subject to UCMJ action and court Martial!