I tried honing and polishing a granite tile that had been sandblasted. When I polished, it had a spotting appearance. Did I do something wrong?

No, you didn’t do anything wrong. When granite is sandblasted the force of the abrasive destroys the crystal structure of the granite. This is why you are seeing a blotchy appearance. Unfortunately the damage has been done and there is very little that can be done to repair the damage.

TIP In a case like this I would recommend flaming the finish. There are available portable flaming devices that will allow you to flame granite in place.