Wouldn't the mimic need Arcane knowledge or Spellcraft, etc. to even recognize that the spell the player is casting is offensive in nature? If it can't recognize the spell being cast, why would the chest automatically assume it's cover is blown? These mimics don't have a very high intelligence level or any arcane training at all.First, I would ask: "Are you sure you want to cast toll the dead on the chest-you-suspect-is-a-mimic? Remember, if it is a creature, the sound of dolorous bells might attract unwanted attention." This may not be directly related to your line of inquiry, but it's really important to emphasize that there is a potential cost to the course of action.
Then, if they decided to proceed and the mimic is able to observe this hostile spell being cast, I would determine initiative. It's possible the mimic might even act first, attacking prematurely as it realizes its cover is blown. How that initiative is resolved is very much a matter to be tailored to each group - my way may not be your way - but I would say some manner of resolving initiative would be in order. (NOTE: there may be exceptions, for example a high level party encountering a single mimic doesn't really need to slow down to the micromanagement scale of initiative rolling)
And then, once toll the dead is cast on that player's turn, it would affect the mimic just as it would any other creature.
.....;D