Last October, one month into receiving may new CX7, both my mirrors were stolen (Viva Mexico!). Mazda Mexico has a anti-theft policy that they would replace the mirrors if stolen (Viva Japan!), max. once per year, to disencourage the black market.
Anyway, I called the dealership and they kept saying that they would replace the mirrors but needed to check the plastic connections that mogulman described, and that if the plastic connections were broken, the complete motors had to be replaced, and the cost exceeded 300 USD (I don't remember if each or both).
Thankfully the burglars were careful enough and didn't broke the connections, so I just had the mirrors replaced at no cost, though I installed anti-theft protection on each mirror, which reduces significantly the vision on the mirrors (some 20%), but they won't be stolen again.
All this sad story intended to say: 1) be very careful if you are going to remove the mirrors, and 2) review that the plastic connections weren't broken during the pillar attack.
I used my CX7 two full weeks without mirrors and the plastic knobs didn't really looked broken, though I couldn't know for sure at that time. The wires were just hanging there, with the terminals ready to be hooked. Once the installed the mirrors in the dealership, the mirror just clicked very easily.