How can I use ClippingPlane to cut the geometry or get the intersection curves?

You can use ClippingPlane to: 

Cut the geometry

• cut a geometry:

  Mesh/Solid/Brep(Solid3D).CutBy(ClippingPlane.Plane);

  For Surfaces:

  Surface.TrimBy(ClippingPlane.Plane, 0.1);

• split a geometry:

  Mesh.SplitBy(ClippingPlane.Plane, out Mesh[] splits);
  
  Solid.SplitBy(ClippingPlane.Plane, out Solid[] splitF, out Solid[] splitG);
  
  Brep(Solid3D).SplitBy(ClippingPlane.Plane, out Brep[] left, out Brep[] right);
  
  Surface.SplitBy(ClippingPlane.Plane, 0.1, out Surface[] splitsF, out Surface[] splitsG);

 Get the intersection curves

Mesh/Solid/Brep(Solid3D)/Surface.Section(model1.ClippingPlane1.Plane, 0.01);