Ok,First of all,Alakazam would kill mime Before mime would get a chance to 
deal out the mounting up damage.Why u ask?Well,for one thing,Even though 
alakazam can't hurt Mime,Yet,He can still confuse the mime,And,as we all 
know,A pokemon power can't be used if that pokemon is asleep,confused,or 
paralyzed,so,if mimes confused,he doesn't have invisable wall.Next turn,if 
mime doesn't retreat or use a full heal,Alakazam could deal thirty 
damage,OR,you could bring out a big pokemon and kill mime with one of those 
little Hay-maker Basic Pokemon that deal quick damage.And since confusion 
doesn't wear off,Mime won't reconver from it if its still active and a full 
heal hasn't come to interfere.