Pipe cutters are a plumber's tool; they don't belong anywhere near a bike.

My advice for someone least equipped to do it: wrap some tape around the top of the bit you want to keep, nice and straight. If you don't have a vice, it'll be a lot easier than a hacksaw if you have an angle grinder with a cutting disk (don't even think about it if it's a 9"), but either way you need to find some way of securing it pretty well while you cut. Start your cut next to the tape, and simply cut away from it a little, ensuring that if you cut off more than you mean to it's no big deal. If you're using a grinder it's easy to square it up now (hold the tool down as an impromptu bench grinder; a fork is light enough to grind with one hand; 4mm cutting disks can take quite a bit of grinding on their side before they become dangerous), otherwise you have to file it down. Put a chamfer around the top, down to the depth of the threads, and use a bit of extra care screwing the cup on the first time.

If you're cutting aluminium, it'll make a bit of a mess, but you can clean the steerer up with a file and the disk with a rock. If you're cutting carbon, forget using a hacksaw or a file (delamination risk), and use a good mask.