
The cut tool lets you split paths.
An open path is one whose end does not join back to its start.
If you use the cut tool on an open path, it splits it into two.
Activate the cut tool, then click anywhere along the path. You can click on an existing point, or anywhere along the line.
A closed path forms a loop: the end is connected to the start.
If you use the cut tool on a closed path, it opens the path at the point you clicked. That is to say, the path now has separate start and end points, however they are in the same location. Because of this, it may not be visually obvious that your cut has worked.