What do you mean by "playing mean"? Is she literally playing roughly, or does she act agressively?
One of my cats used to play roughly when he was still a tiny little furball. It was quite funny to look at... but it was not fun at all when he grew up and kept playing that way... now with considerably more strenght and a better set of claws and teeth. He's not mean, in fact, he's quite sweet, but he somehow didn't grew to understand that he should be a bit easy on the game. This kind of behavior often results in a more nervous cat, because he feels he's being challenged all the time. Picking up and petting her might often be taken as a threat...
If the cat is already an adult, it's going to be hard to change it, so maybe you'll have to respect the fact that it's a permanent part of her caracter.
Try keeping a little treat at hand, so that whenever she plays nice or let herself be pet, you can reward her and make her understand that's the way to please you...

Hope this helps...