Mr. Mime is an invaluable asset to my psychic deck? Why? Because I've
come across a few Charizard in my days as a player, and none of them
have ever knocked out Mr. Mime. Here's how:

Charizard comes out and blows away my guy I have out (usually a
Dragonair). I bring out Mime, and since he's wasted 2 energy on
Charizard, I ER and SER him to prevent him from retreating. I Meditate
for more each turn, and I finally knock it out.

I've had the most success with Mr. Mime, but my Sandshrew once knocked
out a Blastoise =). But that's another story.

Arcanine654