It is important to remember that a toilet is always set on top of flooring and not directly on the subfloor. If replacement tile is being installed, the correct procedure involves removing the toilet, installing the tile and reinstalling the toilet.
When installing floor tiles, mark the location of the drain pipe and water feed, then cut the flooring as needed. Any rough cuts will be hidden by the toilet and the escutcheon of the feed pipe. This looks tidier and seals better than cutting around the toilet base. Setting a toilet on flooring also distributes the weight of the toilet on the floor. Remember to shut off the water supply before removing the toilet.