I am a dual citizen MEX/US. So I have a US and a Mexican passport. My US passport needs to be out of commission for a matter of weeks, and I need to exit the US during that time for travel. I am wondering if I can leave the US on my Mexican passport although it has no stamps in it currently
This is fine. The US doesn't have exit checks, so you won't be subject to questioning or anything when you leave. The airline (if you're flying) will check your passport, so make sure you're going to a country you can enter visa-free as a Mexican citizen (or apply for a visa).
Entering the US, you're legally obliged to use a US passport (or Enhanced Drivers' License, Passport Card etc. if you're crossing by land).