How to cut paper properly with a Katana
Cutting suspended sheets of paper requires perfect edge alignment, speed and an especially sharp sword. Firstly, holding the Katana the right way and correctly goes a long way to ensuring correct edge alignment. And slow cuts almost always fail. You should pay attention to and try to improve at every opportunity. If you apply pressure directly downward in a slicing motion it won't cut paper.
When cutting newspaper rolls that often called 'the poor mans tatami' (bound with string or rubber bands and soaked in water until it is heavy and saturated makes a reasonable), good technique and speed is critical. The level of challenge can be increased by adding a wooden dowel core to the roll.
One good way of doing that is by watching videos of true sword masters doing their thing and simply try to emulate their stance, relaxed posture.