First, soak your yarn in acetone. THEN WASH YOUR HANDS BECAUSE FIRE WILL BE INVOLVED. After that, tie your flammable yarn a bunch of times (like, 20 times) around the spot on the bottle that needs a-choppin'.
Drop a match on that sucker, and poise yourself gracefully over a bucket of really, really cold water. I just happened to have a gallon on hand because I guess that's just my life now. While covered in flames, rotate the bottle slowly to keep the fire consistent. It's kind of like smoking a blunt, or so I've been told by friends who are bad influences and never amounted to anything. When tourists walk by and ask why you are doing this, just tell them it's part of your religion and roll your eyes at their cultural naiveté.
After doing that for about three minutes, dunk your piping-hot bottle into the freezing ice water. The top SHOULD pop off. If it doesn't, take the yarn off, peep your progress, and try the whole thing over again. Like having children, it will be easier the second time around.