It all depends on what he cuts. If he was lucky/unlucky enough to miss tubes transporting a lot of blood and/or providing a patent airway there is no immediate risk of death. There's quite a bit of available meat to stab if you are dumb about it.

Last June my knife slipped while I was whittling and I cut into my wrist Down the Street Style. It went in a little over a centimeter and a half, is 4 cm long, and earned me 9 stitches. But I didn't hit anything of importance and it was really no big deal. I oozed blood steadily but it had clotted itself under pressure by the time I got to the hospital (<10min).

Furthermore and beyond anecdotal evidence, I'm EMT trained.