Maybe someone else knows how to do this better, but I would just pry the nails out carefully. Maybe cut the tack strips on each side of the nails so the full nail is exposed and then use some means of pressing on the Terrazo around the nail as you pry it out.
I wouldn't hold out much hope of getting the nails out without chipping. Maybe a tile store would know of a good patch compound.
Cutting the nails off flush will not work any better, and you would have difficulty grinding them flush without cutting the Terrazo. Plus they may rust in time.