Be very careful when near the griffin. It's very aggressive, and the fastest flyer in the game. If you're a low level with only stone tools, then run like the wind( Try to get into water ). However, it's an amazing tame, so I suggest you should get it.
Please note the like megalanias,wild griffins are aggressive and get attacked by other carnivores,and does zero damage,so u won't hav to worry if a therizinosaurus kills it while taming it.(edit:zero damage to wild creatures)