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.
Definetly top 3 Strongest fliers in the game so its a must have, Get a Pterandon (Or argy but there more valubale in my opinion so I use pterandon) and pick your tribesmate or the other way around and get it to chase you as you shoot it with good knockouts (shock tranqs) cus these things will kill you both or die first so be fast once you knock it out build a fence around it seeing as they are rare-ish so nothing kills it and if your on a pvp server protect this thing if on a beach or open feild chances are someone will end the things life.