Mr. Mime

Mr.Mime is... a thing. It legitimately doesn't have any value beyond "oh look, a regional Pokemon".

Best PvE Offensive Moveset

• Psywave is a stronger option than Confusion that's substantially easier to dodge with.
• Zen Headbutt falls behind.
• Psychic beats out Psybeam easily.
• Shadow Ball is the best move if you want Mr.Mime to act as a generalist, but it's downright atrocious in the role. 
• Magical Leaf does Mr.Mime no favors.

Best PvE Defensive Moveset

• Always use Confusion.
• Always use Shadow Ball.
• Razor Leaf is okay too.
• Zen Headbutt, Psywave, and Psybeam are not good. Psychic is good, but it's generally the inferior option.

Confusion benefits any Pokemon that can learn it. Its 4 DPT (Damage Per Turn) and 3 EPT (Energy Per Turn) can hurt whatever doesn't resist it while building damage quickly. Shadow Ball (100 Power/55 Energy) is a great move with great neutral coverage, while Psychic (90 Power/55 Energy) is actually stronger against neutral targets thanks to STAB.