Designing tile floor mosaics

Okay, maybe I wasn’t clear enough on the first part.
The existing floor tile mosaic which the potter makes seems to be about one-quarter to one third of a block thick, so I assume this means it’s not something I can put together using the Build tools § without digging out the floor and putting bits of stone in their place.
So, if I can’t use the Build tools, how do I go about creating a floor tile the width I want? Is there a way to create a new tile to my specifications which the potter can make, and can then be placed? Or is this something I’m only going to be able to add by modding?
Of course, if there’s a way to make a floor tile mosaic using the Build tools, I don’t know how to do it, so I’m going to need instructions on how to do that. Up to now, all I know how to do with the Build tools is make houses and walls. I don’t even know how to add designs other people have made and shared. Making a floor tile mosaic seems as if it should be different, but if my assumption is wrong, I need to be told I’m wrong.
Hopefully that’s more clear.