If you accidentally sever a spider's leg, will the leg bleed?

It does bleed, but there is a special mechanism that prevents too much loss of fluid. Here is an explanation from a 1957 paper: Unlike Crustacea and insects, spiders autotomize their legs at a functional joint and an account is given of the interesting mechanism by which the joint is severed and bleeding restricted. read more

-- Spider Leg-muscles and the Autotomy Mechanism D. A. PARRY Quarterly Journal of Microscopical Science, Vol. 98, part 3, pp. 331-340, Sept. 1957. Here is Figure 3 helpfully showing the anatomy of the leg, including the way the severed leg stump closes itself off. read more

In the legs of spiders, the femur-patella joint and the tibia-metatarsus joint extend by hydraulic pressure only. Spiders do not have muscles for extending the legs at these joints. Spiders control the hemolymph (bug blood) pressure in the legs to extend them and walk. read more