The existing tile does not go under the original cabinets. So we removed the tile before installing the refrigerator cabinets. It is deeper than the base cabinets beside it, so a few inches will have tile on both sides of the cabinet. Should we cut and piece around both sides, or cut the bottom of the cabinet a few inches and slide a tile under it?

When our wood floor was installed, they cut off the bottoms of all the door trim and even cut out the bottom of the brick around the fireplace and slid the wood under it. It looks much better that way.

Cutting the cabinet isn't a problem, but I don't know how to slide a tile under there without messing up the thinset. How do you do that?