What are the regulations, guidelines, etc., covering a mental health discharge in TRADOC?

I've been depressed for 4 months, following the death of my grandmother, I have reported suicidal thoughts on 3 occasions, one of which was at the ER after my mattle buddy discovered a suicide note I had written. I'm curious as to the likelihood of a discharge

You'll have better luck stating your situation and circumstances than asking a broad question like that. There are literally hundreds of pages of regulations that cross reference TRADOC, IET, Mental/behavioral health, discharge, and whatever other things your case touches upon. You can find all of them with Google.
So, please explain your predicament and we may be able to help you.

I can tell you from experience, I lost my grandpa just after arriving in Kuwait on my way into Iraq. It's tough. It really is. But, if you sit back and see the world for what it is and not what you want it to be, things like death get easier to deal with. Did for me anyways.