Break & Join
Use these tools to either split a keypoint curve or join two curves together to form a single curve. These tool works on regular curves as well as keypoint curves.
Access these tools from the Keypoint Curve Toolbox:

Break Curve at Keypoint
Splits a curve at a keypoint. Select the tool, and then click a keypoint on a curve.

Join Curves
To join two curves at their endpoints, make sure that their endpoints overlap (are coincident), then choose the tool and click the overlapping keypoint or edit point.

Note: You can also join regular curves by clicking on the overlapping edit points at the end of the curves.
