I don't know what the ultimate fate of Garrosh is going to be, but I don't think that Blizzard will have him "executed" after a trial. That's just a little too grim for a game like Warcraft. Themes like capital punishment have never been touched on before, and I don't think they're going to start into it now. And it doesn't seem in keeping with the pandaren culture anyhow.
I guess there might be a trial by combat sort of thing, in which he's slain by his opponent, but I doubt it.
I hope they don't follow some sort of redemption storyline for him.