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To do it totally right, I'd think it would take a lot more effort that it's worth. Glass is actually pretty weak, the trick to cutting glass isn't to force your way through the glass, but to trick it into cracking where you want to. With glass panes you do that by scoring both sides of the cut with a diamond (something super sharp). With the surface damaged, you just have to snap the glass and you get a clean cut. With a bottle, you could only score the outside, but bottles are cheap, you can try a ton of times.
PSA: don't cut glass drunk
then to safely handle the slide, it would be nice to deburr and polish the edge you just made... that's where special equipment would be nice. I guess sandpaper, files, and whatever could do that.
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