Immunity to debuffs + Interruption protection WILL prevent the Mystery from being stopped. Go change to Midnight Blade, take Root of Warrior, put Mifune on the team and activate his Mystery, have the opponent try to CC him. He will still use his Mystery. The only way to stop the Mystery in this situation is with Immunity Suppression and/or Buff Removal (Han/MaskedMan/PeriodKushina/EdoRoshi).

Edit: I have been an idiot in the past, trying to hard CC Mifune's in the Arena who have Root of Warrior, only to facepalm as he still used his Mystery.