I had one of those bottle cutters from the 70's and tried to use it on chapagne bottles. I never had any luck separating the score until, by accident I left it out in the winter. It rained and then froze with a perfect break. I think it was just luck. Like the time a shot a bb into a benedictine and made a perfect hole near the base. That's a lamp now.
I use my Ceramic Tile Saw with the Diamond Blade in it, and it works great..Just make sure you put Scotch tape over entire cutting area to keep glass from flaking when cutting.
I know this thread is a little old but I just thought I would add my two cents here for future reference.
I mainly cut just the bottlenecks. I have been using a wet bandsaw with a diamond blade that works very well with minimal chipping and gives you a precise cut. This is might not be as effective for the base of the base of the bottle. A tile saw as stated above will work. I would get the thinnest blade you can however. Or use a slow rotating motor with a diamond etching wheel. Make sure you continually rotate the bottle so you dont put too much pressure on one side or the the glass will eventually break instead of cut. I emphasise on whatever method you use you must keep the bottle wet. Heat is your enemy. The water will also wash away loose grit and glass. You can create or purchase a drip kit which can aid in water dispensing.
I hope this helps someone.....................BottleneckSlide
THanks for all the info i have purchased a tile saw and it works great. It cut right through the glass well just have to be careful with it. Once again thanks to all with the great info.[]