No. A card becomes a new object each time it changes zones, but Mirage Mirror only changes what it is. Also, even if it did become a new object to fizzle targeting, it loses it's copy ability while it's a copy, so it can effectively only use it's ability once per turn.
November 11, 2017 10:49 a.m.
Mirage Mirror's ability doesn't make it change zones and therefore, it's still the same mirror object, except now with copied values. So, if you cast a bounce spell (e.g., Boomerang) targeting Mirage Mirror, boomerang resolves as long as its target (mirror) is still valid (i.e., mirror does not get shroud/hexproof or change zones, for example). Once Mirror becomes a copy of something, it loses the copy ability, so its owner cannot keep activating its ability, unless the owner activates Mirror's ability multiple times while Mirror has not copied anything yet (i.e., keep multiple copy targets on the stack).