Hard to figure out what to say to this piece.
It will succeed after a couple of houres and a lot of pain...XD
If you cut across the wrist like that, you miss the major veins. If you cut down the wrist though you successfully sever it. It would be ridiculous to do otherwise as a legitimate suicide attempt. If you want to die in the most gory and disgusting way I would recommend cliff diving (or just a high jump off anything really) or to give your body to a pack of boars.
Don't forget, it's down the river not across the stream. Otherwise the job won't succeed.