So if I'm understading you correctly, you broke the zipper on the back of the vest piece and the vest piece with a broken zipper is still on the upper body.
The vest piece does come off, as it is a separate piece from the undershirt. Like Motux stated though, it's extremely difficult to do so but if you keep working at it, it does come off. It's all about the way you position and bend the arms. You're going to be bending and twisting the arms around quite a bit to do so. You may end up sitting there for 20 to 30 minutes working at it.
If and when you do get it off, you can always go the route of just buying a new vest piece on eBay. However, you'll have to go through the same process of trying to get the vest back on the body. If and when you do get it on the body, it's very tight fitting, so the zipper doesn't necessarily zip up that easily. The zippers on these suits also seem to be extremely fragile, and if you try and force it, it usually ends up breaking (as you found out). Then there goes a waste of however much you ended up spending on the replacement vest piece (usually $60-$70 is roughtly what people seem to be bidding them up to when I last looked).
As others have recommended, my recommendation would also be to simply by another upper body, or new body altogether, that already comes with the undershirt and the vest piece attached and zipped up. It's more of a safe bet to me spending the roughly $150 than risking spending $60-$70 for just the vest piece and run the extremely high risk of breaking it again. Then just swap the pants, boots and accessories off of the old body and put them on the new body. All of those parts are easy to take off and put back on. Then you could simply part out the old body and undershirt of you wish.