When a member of the family is diagnosed with cancer, whatever the circumstances, it's a terrifying proposition. That your DP is losing it and probably frightened to death is understandable but not excusable.
Your priority right now is your immediate safety. You need to get yourself to a safe place. Your DP needs urgent mental health treatment, help and care, but this can be sorted once you're safe.
A year ago I was the wife in this predicament. My DH was diagnosed with this cancer; thankfully, like your own partner's situation, it was early stage and hadn't broken out of the prostate. In these circumstances the prognosis is better even for those patients who, like our respective partners, were diagnosed young. It was invasive: there was no question of a 'watch and wait' approach.
This is all good news but the road ahead won't be easy. A radical prostatecomy is brutal. The proposition is is terrifying, the recovery long, and the possibility that this may permanently damage your sex life - or at the very least take a couple of years to resume it - is not appealing to most people. At that juncture, the only thing I wanted was my husband alive and if that meant we never had a physical relationship again, it was a price I'd willingly have paid. After that, there's a PSA test every three months and the wait for the results is excruciating. You live constantly with the fear of it coming back, hard though you try to put it on the back-burder and resume your life.
All this is major stuff. I don't want to excuse his behaviour - it's unconcionable whatever the cause - but the PP above makes a good if seemingly harsh point that it's not helpful to pretend everything's now fine. A year on, my DH has now been referred for psychotherapy, as it's my belief he's traumatised by what was in anyone's language a terrifying, not to mention painful, experience.
I feel for your partner enormously, I really do. But whilst it's harsh to say, you can't even begin to go through all that with someone unless he also shows willing and seeks treatment for his MH issues and alcohol abuse. It's a hard enough road to travel without those toxic issues thrown into the mix. If you decide you can't do this I doubt anyone would blame you, but whatever the situation that decision should be yours alone. Don't capitulate to any attempt at outside pressure.
Very sorry you are going through this 