How small?
down to 3mm you could use a miniature plumber's pipe cutter, the type with rollers and a cutting wheel.
below that, either a very fine saw or use a sturdy blade, like a Stanley, and carefully 'roll' it on a cutting mat to score round the pipe. It is so soft that this method works like the pipe cutter and gives a burr free edge.
Note if you chose a saw - the TPI needs to be so fine that the teeth don't engage on the diameter as such otherwise it will just drag the pipe and bounce rather than cutting. Personally, I use Zona saws at 0,010 blade thickness and down to ~52 TPI with a pull cut can't be beaten.
Finally, you could also use a miniture slitting disc in a rotary tool... ;D