In my fantasy world there's the race of trolls, vastly inspired by the ones one encounters in Baldur's Gate 2 (see here).
Millennia ago, they've been driven underground by orcs and elves, as well as occurring humans later on due to lack in numbers and technological advancement. The dwarves at first tolerated their presence but as the trolls are mesmerized by the sparkle of gold and the resulting raids on dwarven mining sites they drove them back to the surface in a couple of millennia. Now the trolls live in a huge cave system in a mountain and the close outside valley bordered by a river in the west and another mountain range in the north keeping among themselves and travellers off.
They're 2.5 to 3 m (~8'2'' to 9'10'') tall if they stood upright and despite their somewhat sleek look, they have stronger bones and muscles than humans to support the increase in weight. As they spend most of their time in more or less tiny caves they adapted quickly to a bent walk setting them at eye level with humans at most.
They also have a highly efficient regeneration allowing them to regrow severed limbs including the head in mere hours for use and fully in a few days. Even without head their heart keeps pumping and as long as their blood doesn't run cold and doesn't clot their regeneration works. One can slow it down by the use of fire or acid as the fire closes the wound (the key to the regrowth of limbs on salamanders is that their wounds don't close) and the acid eats into the flesh destroying regrowing cells. This is but a temporary solution. Driving a blade into the heart of a troll also can't kill it, as minor wounds get healed quickly enough for not requiring the heart to beat and keep the blood flowing. The only way to finally kill a troll is to cut out his heart since this is the only way to stop the regeneration ability powered by the remaining blood as it takes too long to regrow a heart and thus the blood runs cold.
Is this somewhat plausible to not explain it with "magic"? Is such a high regeneration possible? Could it be explained with an organ responsible for constant stem cell creation or anything like that? Can such a high regeneration ability be able to adapt their walk in, say, 10k to 20k years without causing chronic pain in their backs while also not decrease their size much? What about the regrowth of the brain, how could that be possible? I know I'd have to deal with memory loss. What about the energy consumption. Is it possible to regrow a head without being able to eat? Maybe leave it tiny at first with a very small brain and then regrow according to the amount eaten? Are stronger bones and muscles in combination with their rather sleek look enough of an explanation to make their body size possible? Is there anything else I missed that makes their physical presence impossible? Why do I have so many questions?
High regeneration is absolutely necessary. Their fighting strategy is to catapult themselves with copied ballistas from stolen dwarven blueprints over walls of cities ignoring all the resulting injuries. If they're not able to get back on their feet and start fighting within minutes to few hours, that strategy is doomed.
However, as this would result in bruises, broken bones and other inner injuries rather than cut off limbs, regrowth of limbs can take its time. Also, they do not have to regenerate fully very quickly but only so they're in fighting shape. As they're still taller, stronger and tougher they'd at least not be in disadvantage to humans. Also, surprise is on their side.
Now again the question, would that be possible? Imagine a person falling down a couple of stories on a plastered road, he's dead.
I'm trying to clump together what I got as answers and comments until now. Thanks to everyone so far.
The trolls stay slim with strong muscles and bones making them heavier but also reduce blunt trauma upon falling and give them slight resistance to flails and the likes. Their slimness partially compensates for that. Height also stays the same as nobody knows how large they've been before they were driven off underground, thus the occurrence of a slight reduction could have happened anyway. They have a hard time standing upright and usually do so only on rare occasions like intimidating others or taking a look over obstacles. They have a rather slow metabolism and generally lead a life with less movement than humans do. They train and enslave kobolds to gather food and do any other kind of work such a small being can handle, so the trolls themselves don't have to move as much. If they engage in physical activity they burn their energy quite quickly, so in combat they get exhausted somewhat fast making them a much less dangerous enemy afterwards. Don't get pleased too quickly though, you won't survive that long. This leads them to being great sprinters and jumpers with their long legs but earns them the last place in the New York marathon. Also, if necessary, they eat parts of their enemies to regain energy, they love the taste of human infants even more than the sparkling of gold.
Regeneration: Wounds without removal of body parts like stab wounds or broken bones regenerate rapidly at first. Blood clotting starts quickly and an effective stem cell creation and deployment process generates tissue closing open wounds and stitch together bones within minutes. The latter leads to skeletal deformations in numerous cases. Final healing process can take up days to few weeks depending on severity and requires quite some food and rest. In order to cope with the fast beginning of the healing process trolls have an energy reserve in form of a round belly. Refilling this reserve additionally delays final healing process. This, in combination with a vast distribution of endorphins to suppress the pain, lets them engage in combat incredibly quickly after experiencing physical trauma.
Regrowth: Fast plot clotting and stem cell creation helps with regrowing limbs as well and the process starts quickly, too. The belly fat pad does barely help though, so a disfigurement leads to the troll instinctively evade the battlefield, thus desertion is no rarity. Once out of danger the injured needs a lot of food and rest. Regrowth takes few months up to a year. If possible, hours to days later the body enters a form of hibernation, only interrupted to eat, speeding up the process vastly (maybe half the time?).
Beheading: Now to the fun part. Upon decapitation the body immediately shuts down any non required functionality. Loosely coupled brain cells scattered across the torso adopt control of the organ functionality, which is absolutely required to keep the body alive. This makes the body nearly impossible to kill as you have to destroy it entirely in order to prevent it from functioning. Rudimentary redundant memory cells enclosed in the spinal cord store basic memories so the regrown brain doesn't start at zero, body functions like walking and important personal memories forming the basic character. It would be possible a beheaded troll becomes a different one if their "society" would actually encourage personal individuality. The scattered brain cells in the torso are also able to weakly process optical stimulus, so the first things to regrow are eyes and mouth so the troll can identify, consume and process food to gain energy. From then on the hibernation state mentioned earlier is the way to go with the full development of the brain being the last to occur, as it takes up to several years to fully function correctly. In the process, the body can manage more and more activity so the sleeping phases of the hibernation state shorten after some months. In the early time the troll behaves very animalistic only trying to satisfy the most basic instincts.
In all three cases the blood stream takes control of the stem cell distribution, so the troll can't regenerate anymore when you cut out his heart. Also, before engaging in combat they eat as much as they can to gain a highly possible energy buffer.
Does that sound plausible now? The only problem I currently see is the energy consumption until the mouth has developed. What about photosynthesis and water? Could that give the body enough energy to slowly heal if not doing anything else? How about collecting necessary nutrients through the skin?
EDIT 3: I've finally managed to write it all down and will mark Hankerecords' post as answer as it has helped me the most. Thanks to everyone for helping :)