It doesn't. At least, not directly. What it actually does is stimulate ever single nerve ending simultaneously. Nothing more than a brushstroke, which is why a single instance leaves no trace, but applied across the entire body, at the same time, it's enough to make the victim wish for death.
Which is how it affects the soul.
From what I've studied, there are two things that cause death.# One is that the heart stops. The second is that the soul separates from the body. When a victim is subjected to Cruciatus, their body's response to that sort of pain is to try and escape it by...
...well, by dying, in the absence of all other alternatives. Either through what the Muggles call "cardiac arrest" -- which, unlike the petrificus cardis, can be reversed -- or by severing the soul's connection to the body.
There have been tests conducted on Muggles in less... enlightened times. And it was observed that when the Cruciatus was repeatedly applied, the victim's body attempted to achieve death.
*small smile, not in any way indicative of amusement* The findings imply that the victims whose hearts gave out were the lucky ones.
I suppose technically there are two. One was the cafe. I don't think the building itself vanished, but the Cafe, its owners and quite a lot of its patrons seem to have. The other place is a pub which, as far as I'm aware, is still around.
*something occurs to him* Although it's been a while since I was there last.
#There may be something to do with lungs shutting down as well, but I'm not really in the mood to google death so for now, we'll just assume Sirius has covered all of fundamental causes of death. *brushes loose ends under a carpet, and walks away whistling the "nothing to see here" motif*