Dear Pojo,
    I've found the ultimate Mr. Mime killer.  Nidoking!  He is the only card
that can kill a Mr. Mime in one hit while his pokemon power is in effect. 
Using his Toxic attack he can do 20 damage and do a 20 damage-indusing
poison.  Mr. Mime (a 40 HP basic) takes 20 damage from the attack itself and
takes 20 poison damage for the after turn check.  It's that simple!
Here's a readout of Nidoking:

90 HP(Holo) Evolves from Nidorino   Type:Grass

GCC Thrash: 30+ Flip a coin.  If heads, this attack does 30 damage plus 10
more damage; if tails, this attack does 30 damage and Nidoking does 10 damage
to himself.
GGG Toxic: 20       The defending pokemon is now poisoned.  It now takes 20
damage instead of 10 after each players turn (even if it was already poisoned.

Weak: Psi       Resist: None    Retreat: 3 Energies

I know that Mr. Mime is Nidoking's weakness.  Just charge him up on the
bench.  And here's a great deck idea: Toxic Death.