Sometimes, the wall has a little plaster or paint hump that rejects your mini cutter like a bouncer at a club. Solution: break out the oscillating multi-tool. This weird, vibrating blade is a miracle for cutting flush to a wall. It looks like a dental tool for giants, but it works.
But here’s the real pro move: use a pipe cutter with a swiveling head. Some models let you pivot the cutting wheel so you can cut at an angle, bypassing the wall bulge. If you don’t have one, just use a file to carefully notch the wall back a quarter inch. The Sheetrock gods will forgive you.
I once cut a pipe so close to a tile backsplash that I chipped a tile. My wife still brings it up at dinner parties. Avoid my shame: tape a piece of cardboard over the tile before you start.