- Are you asking about the mythological/legendary creature also known as Gryphon?
If so, this would be the creature which has the head and wings of an eagle, and the body of a lion. The gryphon was generally known for guarding treasure.
If I'm remembering my mythology correctly, gryphons eat most anything, including people.
- If you are asking about the griffon Dog Breeds--well they eat what any dog breed eats.