I remember when bottle cutting kits were all the rage back in the 70's. There was a gizmo that fit in the hole, and a glass cutter you went around the bottle with. Originally, you were supposed to tap gently around the scored line until it separated, but that method was unreliable, especially with larger items like gallon jugs. We used to fill the bottle with motor oil up to the score line, then stick a red-hot iron poker into the oil. You'd hear a 'click', and the top would be separate. Messy process, but very clean cut. My sister liked to cut gallon bottles to make food and water dishes for her cats. We would sand the edge smooth and take the sharp edge of with sandpaper.
I remember I was quite proud of my set of juice glasses I made from Michelob bottles.