Well the body doesn’t kill itself, it’s just that eventually it doesn’t have any way to generate more heat and your insides where your organs are gets so cold that they can’t function anymore. Before that it will sacrifice your extremities and let your outer skin and stuff die to keep as much as heat as possible deep inside, since you can still survive if some extremities or patches of skin die but not if your heart stops beating.

The stages of hypothermia are defined by your body temperature. Stage 1 is around 90-95 F, you’ll shiver a lot and feel freezing but otherwise mostly normal. Stage 2 is around 82-90 F and you’ll stop shivering and start to become delirious or lose consciousness. Stage 3 is around 75-82 and you’ll be unconscious with weak vital signs (your heart is barely able to beat anymore). Stage 4 is 59-75 F, you’ll appear dead but it’s possible that you might be revived. Below 59 F and you’ve definitely frozen death. How long it takes depends on a lot of things, like the temperature outside and what you’re wearing. That’s why you might see warnings about hypothermia and dressing appropriately when it’s really, really cold - like if its -50 F, your body temperature can drop into stage 1 hypothermia in less than 5 minutes if you aren’t covering your head and hands and feet.