Hi,
You cannot split a sketch without editing that sketch which is bad workflow. Once you create a sketch you should
leave it so that you can follow things later more easily. Sketches should always be simple and only try to do one or
maybe two things, they are used for creating and modifying your Model.
What you can do is create a new sketch and then Project portions of another sketch into the new one. This is
especially useful if you are using the Design in Place method where you might want the outline of an existing
component or a centre point that you then use to design the next component.
To use the Project tool press P when in the sketch. The sketch you want to project into the new sketch must be
visible.

Projected geometry will be purple as you can see in my model above. Projected geometry is also used in the new
sketch to define the rest of your sketch. A projected point is treated like an origin in the new sketch and you can
dimemsion the new sketch in relation to the projected points.
Cheers
Andrew