Rent or buy a commercial-grade wet tile saw. Since these are expensive power tools, unless you plan to cut bottles on a regular basis, renting one is a good idea.
Wash the bottles, removing any existing labels. The saw will easily cut through a label, but the label may obscure your view of the cut.
Determine the location of the cut, often just under the neck of the bottle, and adjust the guard on the wet saw to match that length.
Slide the bottle carefully towards the moving blade of the wet saw, keeping it along the flat surface. The saw should be running at full speed. As the bottle nears the blade, a stream of water will spill onto the glass, keeping the blade from heating up.
Gently roll the bottle against the movement of the blade in order to cut around all sides evenly. Once the blade penetrates the surface of the bottle, begin the rotation. Hold firmly to the bottle and rotate it at a steady speed.
Use the sandpaper to smooth the edges, starting with the medium grit and finishing with the fine grit.