I was actually quite surprised that nobody mentioned these simple PVC saws when someone requested a cheap PVC cutter awhile back. I’ve been using them since high school, and haven’t found a better solution.
Basically, you slip the wire around the PVC pipe and start working it back and forth. It seems to melt through the pipe once you get going, which means less dust and a smoother cut than other saws I’ve tried.
It also has an advantage over other dedicated saws due to its flexible nature. I actually used one of the longer versions to cut a bit off of a kitty litter box once (it had a spot to hold a scooper, which made it a bit too big for the space). That would have been impossible with other PVC saws that hold onto the pipe. It also would have been tricky with a hack saw due to the size.
At less than $10 for even the most expensive ones, it’s a great thing to pick up for an occasional job. And not that painful if you end up losing it.