Take a piece of masking tape and wrap it around the base of the bottle neck, making sure one side of the tape makes a perfect circle surrounding the neck. This will serve as the guiding line for the glass cutter.
Using the glass cutter, scribe a solid line around the neck, following the tape guide line. Make sure the line does not break or get choppy going up and down the neck.
Remove the tape.
Take the bottle to the kitchen sink and run very hot water, for two (2) minutes, over the scribed line on the neck.
Here's the trick! Change the tap water to cold and run the neck under the stream ... AND TAP ON THE SCRIBED LINE WITH YOUR FINGER or the metal ball end of the glass cutter. Slowly rotate the bottle, allowing the water to hit every part of the scribed line. You should eventually hear or see a crack along the scribe. The neck may even fall off (you may want to place a towel in the sink before this step, to keep from breaking the neck.) If there is no crack, repeat steps 4 and 5.
If it cracks but the neck does not separate, take hold of the neck and snap it off (just like breaking a chicken's neck.)
Dry off the neck and use a Dremel rotary tool grinding bit to smooth the edges of the cut glass (or, if you are a purist and want the slide to be 'authentic' to blues history, take it outside and smooth the edges on your sidewalk. Be careful not to chip off too much in the process.
Voila! You have your own true blues bottleneck slide.
Don't get pissed if your first attempt doesn't break right. This happens from time to time. Keep practicing.