I know there's code requiring torso or head reduced to 0HP for a kill...but losing all four limbs in one encounter really ought to do the job based on massive trauma, bleeding, etc.
Under the hood, after multiple amputations, you're probably looking at around ~10 points of health remaining at the absolute most, probably less, and losing several points of health per round of combat. So if you do manage to incapacitate an enemy after multiple limb loss, and then grab them and haul them off site for conversion, you'll have to be extremely close to the exit or the hostage will bleed out and die before you get off site. If you do get off site, you can probably stabilize them; while it's technically possible for people to die from injuries back at base, the game is very forgiving about that.
The head/torso shot needed to kill rule is just that limb attacks can't instantly reduce a target to 0 blood and kill them. It prevents a shot to the arm from causing them to suddenly drop dead. When someone loses a limb from full health, they will end up anywhere from "about half health, occasionally missing turns, but mostly able to fight assuming they still have arms" to "so close to death that they die before their next turn even if nobody hits them". If they're already chewed up when the arm or leg is blasted off, such as from having a previous limb removed, they're pretty certain to be a blubbering mess afterward, and will probably die very shortly.
I actually think Toady's system for location-based damage in LCS is really well done, since, aside from excessive limb removal, it has pretty intuitive results with regard to severity of location-based damage.