The absolute BEST card for killing Mr. Mime is This:

NOT Muk!
NOT Lapras!

It's NIDOKING! Yes! The single best card to pull out against an
'Invisible Stall'! Now, it DOES have a weakness to psychic, but if you
play you cards right;), you'll never get hit! Use his Toxic attack(20
damage, followed by 20 poison damage) to blow up Mr. Mime, and you will
do fine. Even if they GOW for it, they'll still need a psychic Pokemon
to do 50 damage to knock it out.(watch for Kadabra) It DOES need a grass
deck to be in, but just use non-poison type Pokemon in it, like
Bulbasaur and such. There you have it! Stop those stallers dead in Their
tracks! And you have Lord Gothmog to thank, for bringing this wondrous
information to you!

Lord Gothmog, Pokemon Master.