This is a video from the PBS series Deep Look discussing how daddy longlegs can purposefully release their legs (a form of autonomy -- like a lizard losing its tail) to avoid predators and live to creep out my girlfriend another day.
Daddy longlegs' appendages don't need to be pulled off because these arachnids, related to spiders, drop them deliberately. A gentle pinch is enough to trigger an internal system that discharges the leg. It's a way to stay alive in the wild if something is trying to devour the bug's limb.
If you skip to 2:45 in the video you can actually watch a scientist gripping the legs of a daddy longlegs so it releases them and he can study how it learns to walk without them. They seem to do fine all the way up to losing three legs. What happens if they lose more than that? My guess is things get a whole lot sadder, especially if all the legs were from the same side.
Keep going for the video.
Thanks to Dip, who agrees if daddy longlegs were really smart they'd learn how to grow those legs back like my uncle did with his finger after cutting it off with a table saw. I think he used pixie dust.