Claymen are creatures that are created by the Pigmasks from...clay. They are used for security and movement purposes. If they are a failure, they will immediately be thrown into the Garbage Dump after being taken to a large pile to see if they can revive them. If they can, they will be sent back to work.
The Claymen appear in Mother 3, and only appear every once in a while. They do have a few big roles in the game though. In one chapter, you will play as Lucas while Boney goes off to exercise, and you will have to find Tired Claymen and take them back to the beginning of the building. You also have to fight them every once in a while. They are usually defeated by Wall Staples, but they have High Defense, and usually pretty high HP and Atk.