Are there any airports which use a metro to transport cargo?
DFW Airport's original train system had cars built to carry mail and luggage.  Most of the system was never used because it was slow, and there were worries that it was hard to train employees to interface with it. I would guess that a lot of airports have not tried such as system because their trans are optimized for passengers, so it is faster to just move luggage across the tarmac on trucks. 

Edit: Jonathan Walters mentioned that Denver also had a system, but it was buggy so they stopped using it.