Actually, those pinchers are called pedicellaria and you have done very well to photograph them!
As James correctly notes, pedicellaria are part of the seastar. They are also found on some sea urchins. In seastars, pedicellaria are "two-jawed" and in urchins, they are "three-jawed." One species of tropical urchin with only has a few spines actually has highly poisonous pedicellaria which have killed people handling them (Look out for Toxopneusta sp).
It is generally thought that the seastars use the pedicellariae to keep themselves clean free from fouling (kinda like a really aggressive antifouling system) by picking off anything that settles (eg. larvae) on the surface on the animal. They are essentially a modified version of the spines on the seastar surface and act like little pincers as you observed.
I'm not quite so sure about the sea cucumbers id by Matt, but I'm happy to be proven wrong. To me, they look more like a member of the phylum Cnidaria, but being an Aussie, and never having seen them before - maybe I've just got things topsy turvy?? 