I've heard it said various times that the body's tissues will begin to necrotize after being cut off from the blood supply for only a few minutes, but that can't be true.
A few years ago, I woke up one morning and apparently I'd been sleeping just right so that the main artery to my left arm was totally pinched closed, because it was completely numb. Not just "arm's fallen asleep", either; I had no mental control over the entire arm and no feeling in it. I could lift it up with my right hand, and it would fall back down immediately when I let go of it, and I didn't feel anything when it landed on the mattress. It kind of freaked me out at first, but in just a few minutes I felt the "pins and needles" feeling of circulation returning, and it was 100% back to normal within less than an hour.
Given that I had presumably been sleeping on it like that for several hours, and yet I somehow didn't end up with a dead, useless arm that needed to be amputated, I know from personal experience that tissue doesn't die within a few minutes. So how long does it really take?