Probably not. Dogs, bears, cats and their relatives in the mammalian order Carnivora have carnassial back teeth, which they use to cut meat these teeth are closely spaced and have sharp edges. They work as a sort of scissors. These teeth can indeed cut off a finger if the animal is big enough. A lion or a big dog can cut a finger off. A house cat may not. Nevertheless a house cat's back teeth can cut the hard and dry cat food nuggets easily.
Sperm whales are toothed whales, the largest toothed whale alive, larger than dolphins and the orca. The baleen whales like the humpback are larger but they lack teeth. Their baleen plates are made of keratin, the same protein found in hair and finger nail. The plates are used to filter small animals from the water, not to bite. Even though toothed whales have teeth, their teeth are generally not closely spaced and they are used for gripping and crushing, not cutting. It is therefore unlikely that a bite by a toothed whale can result in a finger being cut.
BTW, the giant panda also have ancestors with carnassial teeth that can be used for cutting. But since the panda has evolved to eat bamboo, those back teeth have evolved to have blunt edges, instead of very thin but sharp edges, making them stronger when chewing, since bamboo is a lot harder than meat. The giant panda uses the back teeth to cut bamboo instead of meat. If a lion tries to chew bamboo with its back teeth, the teeth may lose its sharp edge and/or the tips of the teeth may crack.