1. Make trap, place trap usually a 4 stone gates with equal distancing and 2 gates obviously.
2. Kill everything around trap, the griffon will go after anything and it will be a hastle trying to get it follow you.
3. When you get griffon to follow you make sure to get close by trap when he starts so he gets in when he first hits you. If your far away and then he catches up to you he will fly around you and not go into the trap.
4. Once griffon is traped make sure to get some sort of protection around trap just in case a carno spawns in or anything you know how ark is.
5. Tame it and have fun
Just build a 2x4 or 2x6 pen with a dino gate on one side, placing stone pillars on the outer edges all along it. Make it near the green obelisk! Then fly the griffin into it thru the door with a pteranodon, fly out thru other end thru the pillars, land your mount, run to the other side, close the door, boom. Trapped griffin. Then tame with roughly 150 tranq arrows. Use mutton or prime meat as they are easiest to come by.