The Bloody Limbs are a key item found in Extra Mode on the 1st Floor. They are found in the Scissor Room inside a bloody dresser, after escaping the Giant Teddy Bear. They are the replacement for the Teddy Bear Limbs that you give to The Cook.
Instead of accepting them however, he will tell Viola that they are filthy and would prefer her limbs and then he'll chase her.
When you return to the kitchen after getting the Silver Key, the limbs will be sitting in the sink, though you won't be able to take them with you.