Flying to Mexico (or other country where Mexicans don’t require a visa) on a Mexican passport isn’t a problem unless you get stopped by US law enforcement for other reasons while attempting to fly out, but that kind of problem flying out is not generally applicable unless subject to arrest.

Getting back to the US with just a Mexican passport? This won’t generally work if trying to fly by commercial airlines. For flying back to the US, you would need something from the US Department of State, thus needing to visit a US consulate/embassy. Getting back to the US via land crossings should work, but then there is the issue of proof of US identity and citizenship; and that is where the variability in results is greatest/worst.