The rules, in this case are pretty clear. The spell never mentions mirrors or reflections, it “summons illusory duplicates." Spell names aren’t indicative of their mechanical effect. See Chill Touch.
There’s also vampire wizard statblock that has Mirror Image on its spell list.
It would be funny if the spell just failed though.
That's based on the idea that vampires are weak to silver, right? In D&D, they don't seem to have that weakness. It should be werewolves, devils, wights, jackalweres, wraiths and night hags that don't have reflections in silver mirrors. Also, the mirror in equipment is steel. The only way to get a silver mirror is to learn Sanctuary and have a component pouch.
I'll mention that on my next strongly worded email to WotC
Well, you could just buy one.
I've read something along the lines of it being because silver is a "noble metal" (or something like that) and vampires are unholy/foul creatures, somehow making them not be reflected by silver mirrors