Griffin is a mixed martial arts fighter. This sentence comes from an article about MMA:

The reason why we love Griffin so much is because of his willingness to leave it all in the cage.

What does it mean to "leave it all"?
Without further context, I take it to mean that the emotions -- the animosity -- and the conflict are not carried forth into the real world following the contest.
That is, the combatants may in fact be best of friends, and may work "hand in hand "on the "outside" to promote the sport..
I understand. Thanks.