If you’ve got a few more dollars to spend, buy a flush cut pipe cutter. These are designed to cut pipe flush against a fitting or a wall. They look like a small pair of pliers with a cutting wheel on the side. The mechanism lets you cut without swinging the tool in a full circle.
I bought one after a particularly bad day under a kitchen sink, and it’s become my secret weapon. It cuts copper, PVC, and even thin steel. Seriously, I now look for excuses to use it.