It should come as no surprise that crabs do in fact have blood. However a crab’s blood is much different from mammalian blood because their physiology is quite different.
All arthropods like crustaceans such as the crab and even arachnids such as the spider have a watery fluid called hemolymph which fills the inside of their shell. Their internal organs float freely in this fluid which resembles something of half blood and half sweat. Like sweat, it is a mixture of water and various electrolytes such as salt. Like blood, it has oxygen carrying proteins however they are not bundled into cells such as they are in humans and the crab’s blood is also blue, not red.
These oxygen carrying proteins are known as hemocyanin and they help carry oxygen to the blood as they float freely within the hemolymph and use copper. Oxidized copper is blue, thus resulting in the blue color of the crab’s blood. This fluid is kept circulating by the contractions of the arthropod’s legs and a long tubular heart that is open ended and also runs along the creature’s back. It sucks fluid in at the tail end to pass it to the head end, sort of similar to the way an aquarium pump works.
If you are a crab owner of a crustacean such as land hermit crab it is very rare that you will ever see blood on your hermit crab because any time a wound is bad enough that it does not quickly clot, the crab tends to drop that wounded limb to avoid bleeding to death. This rare occurrence of discovering blood on crabs and their physiological differences that make that blood so much different from mammals could be the reason many think to ask this question.