Parts that you will need:
1) ~2 feet of 2x4.
2) Small sheet of plywood. The exact size isn't real important but it needs to be about 6" longer than the longest bottle you want to cut and 6" wide. My sheet is 2'x6".
3) Plumber's epoxy putty (~$2 at your local hardware store). You'll need ~ 1 oz.
4) Cheap glass cutter ($6 on Amazon).
5) 0.25" bolt, 6 inches long.
6) Wing nuts and two large washers for 6-inch bolt.
7) Rubber leg tips ($1.50 at Home Depot).
8) Five 3" wood screws and one 1" wood screw.
9) Small washer that can fit inside the rubber leg tip. I used a plastic one.
10) Small cloth rag.
Tools: The normal stuff like drill + bits, screwdriver(s), and saw. As noted above you'll need a bit that can drill metal.
Step 1: Bottle Stabilizer
1) Cut a hole into the bottom of the rubber tip. You want the hole just big enough to fit the 6" bolt.
2) Insert the bolt. We want the tip to be able to rotate freely so we need to in insert something to keep the epoxy from binding with the bolt. Stuff a washer into the rubber tip so that it lays flat against the head of the bolt.
3) Cut off a good chunk of the epoxy and knead it so the two parts mix up well.
4) Stuff the epoxy into the rubber tip as tight as you can and form it into a rounded cone.
Set it aside to allow the putty to harden.
Step 2: Build the Frame.
2) Drill holes in the bottom of the plywood and screw in the longer 2x4.
3) Use your bottle to get a rough idea where the hole for the 6" bolt should go and mark it on the smaller 2x4.
4) Drill the hole for the 6" bolt. You want a snug fit so that the bolt doesn't wobble.
5) Attach the 2x4 to the plywood using wood screws.
6) Put a wing nut and washer on the bolt, insert it through the hole, and add the other washer and wing nut.
Step 3: Attach the Glass Cutter.
1) Drill a hole in the handle of the glass cutter large enough to encompass the 1" wood screw.
2) Knead some more epoxy and add it to the handle of the glass cutter. Press it down against your frame so that the cutter rests on the fame and the epoxy. Keep in mind the orientation of your glass cutter so that the tip will press against the bottle.
3) Use your bottle to determine a good spot for the glass cutter.
4) Screw the cutter to the frame and form the putty around the handle to keep it steady.
Once it hardens you're ready to go! You can adjust the stabilizer with the wing nuts so that you can cut different length bottles. You could also potentially move the glass cutter around by drilling multiple holes.