Make sure you trap the griffin, it will fly in a circle around you and be annoying. What you need for the trap...

Griffins can damage wood, so don't use it. Use stone...

1: 4 or 5 stone dinosaur gateway's

2: 2 stone dinasour gates

To tame it...

1: 3 allo kibble

2: a 10x soothing balm

3: a trap

4: lots and lots of narcotics or bio toxin

5: tranq darts ( tranq arrows work too, but not as affective )

Hope this was helpful :)