The mythological griffin could be seen as an example of this. Part lion (king of the animals) and part eagle (king of the sky) would make it rather awesome for the medieval noble class.
The chimaera. It's a lion. And a goat. And a dragon. Why? Just 'cause.
One could argue that it was thusly named so as to provide the title of an NCIS episode, solely for the purpose of the fantastic line, "They did not name it 'The Puppy.'"
… because they named it "the she-goat."
Ancient Egyptian Mythology had creatures like this. They were made up from the parts of ferocious and dangerous animals to, well, depict them as ferocious and dangerous.
Tawaret had a lion's head and limbs, a pregnant hippopotamus's body, a crocodile's backside and tail, and sometimes carried a knife. She was a goddess that protected pregnant women and new mothers from any complications.
Ammit had a crocodile's head; the mane, front body and legs of a lion; and the hind body and legs of a hippopotamus. She was a demon of the underworld who ate the unpure hearts of deceased ancient Egyptians, thus damning them to nonexistence
The Nue of the Japanese mythology has a monkey's head, a tanuki's body, the legs of a tiger, and the tail of a snake (or alternately, a snake as tail). To complicate matters, it is said to have the call of a thrush, which at a certain period of time is also called Nue.
Middle and Eastern Europe folklore of the 16th - 17th has an undead creature named "shroud-eater" or "chewing dead", which is a not-so-dead buried corpse who is eating its shroud (or its own flesh) because either because it is hungry or cannot leave its grave. It is the ancestor of the modern vampire, but shares some similarities with Revenant Zombie (they mostly pestered their own family) and a kind of Flesh-Eating Zombie which can also drink blood. Oh, and their shroud-gnawing was though to spread plagues. Zombie-Vampire-Plaguemaster, if you want.
Believe it or not, most traditional abrahamic angels. Cherubim are described as tetramorphic creatures with four heads, one human, another that of a lion, another that of a bull and another that of an eagle with four avian wings, basically what happens when you mix all the "holy beasts" together. In 2 Enoch, there are angels with a lion's body and a crocodile's head that live in the Sun, clearly following the gryphon shtick to showcase the most badass creature around.