A friend of mine was helping me with a plumbing project and, while at the hardware store getting supplies, he insisted that I buy this General Tools brand, Model 481 deburring tool. Once we started on the project and cut some copper pipe I realized why he insisted.
The way it works is that the blade swivels freely in the head of the tool and this allows you to rotate the tool easily around the inside (or outside) of a pipe and shave of that tiny ridge of material left when cutting the pipe and any burrs. After a couple spins the pipe end is nice and clean.
It works well on copper, steel EMT, PVC, etc. I’ve even used it to shave down rough edges on cut-outs in sheet metal (like on computer cases, electronics project boxes, etc).
Some copper tubing cutters come with a sort of triangular deburring tool on the back of them, those end up trashing the end of the pipe. Ignore them and buy this tool instead.
One word of caution, with this tool it’s easy to apply force to the inside of a pipe end and with soft copper it’s possible to flute out the end of the pipe to the point where it won’t insert in fittings. Just take it easy; it requires very little force to do its job.
The model I bought came with two different blades and has a threaded cap on the handle so you can store blades inside. My blades are holding up fine after deburring dozens of pipe ends, but I suppose if you used it day-to-day you might actually wear one out. Searching online I see there are models that come with many different blade styles and types depending on material you are cutting, metal handles, cases, etc. A professional using this tool every day might have reason to prefer those, but this inexpensive model has exceeded my every expectation.