Cover your counter and put on a mask and safety goggles. Cover your counter with plastic sheeting to protect it and make cleaning up easier. Put on a pair of safety goggles to protect your eyes against dust. Finally, put on a mask suitable for working with fine particles. Most dust masks and respirator masks come with a description of what they are used for, such as sanding dust, aerosol, etc. Choose the one for dust.
Make the marble tiles where you wish to cut it. A pencil may work just fine on a slate or ceramic tiles, but if the wood tiles is glazed, you should switch to a marker. Try to be as precise as possible for this step.
Cut along the top, bottom, and side edges. If you need to get inside the wall tiles, then you should cut through the dry wall as well. A dremel rotary cutter with a diamond tiles design blade will work for most polished tiles.
Use an oscillating cutter to cut through tight corners. While a dremel rotary tool will work for most lines, it won’t work on tight corners. For that, you should switch to an oscillating cutter instead. You may have to experiment before you find the right one for your type of tiles. A multi-surface blade seems to work better than cement tiles blade, however.
Pull the small tiles away. Wedge a thin knife or spatula behind the tiles and pop it out. If you had to cut through the wall, try not to lose anything inside the wall. Your hole is now complete and ready to finish.