Wooden dam for cutting ceramic tile

I just squirt a circular dam of latex caulk around the area to be drilled. I've done hundreds of holes like this. Drill slow with the drill press and don't put a lot of pressure on the tile. Some tiles are soft and easy others are hard and brittle. You can drill cups and teapots like this as well. My wife likes to make tea cup and pot totems as yard art. I cot cups in half for her to stick on some of her wall murals as well. some shots of one in our kitchen. A 1/2 cup as well as some family photos glued on to the backs of tumbled and polished glass, The Scotties and Geckos I cut out of tile with a Ring saw.

Brian, I wish I had a cnc router table right now . Not sure if it’s possible, but I’d like to have these mosaic tile blend in with the main tile . But I’d say this is an impossible cut for tile , but if I had the tile in a water dam system with a small diameter tile bit , I think it might work .
Then there’s making the vector

Hi Rick,
I have cut many small holes without bothering with a water dam. Have used carbide hole saws and diamond core type bits - the former start easier, as there is a pilot drill bit, like with a regular hole saw.
As Brian says, it depends on the composition of the tile body, and the hardness of the surface layer. If you do not use water, and the bit starts smoking, you are overdoing it. Keep overdoing it, and the bit and the tile start glowing.
The only time I have made a 4-inch hole was for a toilet waste pipe - drilled a series of 6mm holes around the perimeter, then used a 4inch carbide-tipped core cutter with a centre pilot. The tile was already adhered to the wall- no problems(but we have solid masonry walls in this part of the world.

Your blending exercise looks ambitious regardless of technology. However, if you simplify the ends of the mosaics a bit (fewer separate endings, no very thin tongues), it is doable with a diamond saw - cutting slits in from the edge like for a featherboard, then scoring between the slits with a carbide or diamond tile scorer, and snapping off the waste bits. Oil up your patience, and be prepared to waste a couple of tiles- typically on the last cut or snap. Leave relatively wide tongues at the outside edges of the tiles - they tend to break there when you are seating the tile.