A lot of that is just typical zombie durability. They’re animated by magic, not by natural body functions, so blood loss or severance of nerves isn’t going to cause them much of a problem. Their body can still be damaged to a point of uselessness (can’t really fight if you’ve lost all your limbs), but for the most part, a sword through the gut just results in this:
As for actually killing them… I can’t speak for every single DK character to ever exist, but there are quite a few ways to destroy them!
Some of them have their souls bound to their weapon, making it a very simple matter of destroying the blade. They’re magically protected and don’t easily shatter/crack, but for those with this circumstance, it’s a straightforward and vulnerable weakness. This was how Arthas was destroyed– Tirion shattered Frostmourne.
If this is the case, and the body is completely destroyed (like, exploded) but not the blade, there are two likely outcomes: the soul remains in the blade as a dormant sentience that could influence future wielders, or the soul is simply devoured by the blade’s magic because it wasn’t being fed by battle. Either way, they’re not too much of a threat if they have no body.
Other players place less importance on the blade (blah blah 2nd Gen vs 3rd Gen differences– vampiric named blades vs. self-crafted blades like the opening quests. Written a lot on these and it’s in my dkrp tag), so it’s just a matter of completely destroying that body.
The most obvious method of destroying is holy magic. As with other undead, their soul is bound tenuously to their body by shadow, and flooding them with holy magic will purge the shadow and sever the connection. It is also noted in the Sylvanas short story that being pierced by Saronite can sever an undead’s soul from its body. A skilled shadowpriest might also be able to manipulate that magic into a severance. Getting rid of the soul is key– remember the Black Knight? He was empowered by the Lich King, but he’s definitely a worst-case-scenario for how durable they can be and how little they rely on their body function.
If you don’t have these options, you want to be left with as little of the body together as possible. Fire is recommended. Beheading is a good start, but you might just end up with a Headless Horseman scenario– best to take off the other limbs, too. Or crush them under something.
It’s possible to also over-exert them. If they’re expending more runic energy than they’re gaining, their regeneration will fail them and they’ll be no more dangerous than your typical zombie. This is how Saurfang was destroyed– a roaming gaggle of weirdly-dressed heroes came into the Citadel and pulped him up for his lunch money.
Don’t try to kill them with anything that requires breathing (deadly gas, drowning, asphyxiation), poisons, starvation, or bleeding. You will be disappointed. My suggestion? Tie them up and chuck them at a Naaru.