Some pipes are in spots too tight to fit a saw or other tool for cutting. String line, a cheap, sturdy nylon string can get the job done and quickly saw through other things like rope too.
In this video from the Essential Craftsmen YouTube channel, you'll learn how to use string line and see how well it actually works. Just string the line underneath what you need to cut and alternate pulling each end. The line cuts through so easily because it's slightly abrasive and the back and forth motion causes friction and heat, which melts through plastics easily.
String Cuts Plastic [YouTube]