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.
On mobile you have to either
a)be level 85+-95+ depending on difficulty
b) buy the crown which requires the primal pass and 100+ amber
c) have your name end with a surten syllable (look on yt/Google for the options) and be level 40+
If you don't do that then the Griffin won't eat when unconscious.
Sorry for th long tip.
DO NOT attempt to kite these with an Argent, I almost lost my best mount to one because we couldn't fly fast enough to get out of its attack range. If you run into one, my best suggestion is to turn tight circles as you fly up, which thankfully I figgured out with just a sliver of health left.
I guess I'll save the kiting for my best pteranodon from now on.