SketchUp is essentially a face modeler. There will never be anything inside. If you cut the thing off you need to create a new face at the cut. Just as with cutting a piece of wood, you never see anything but the exposed surfaces. Wtith Section Cuts you can use Section fill to hide the opening. In practice it doesn't matter that there's nothing inside the volumes.

Thanks for your answer a very long time later I hadn't passed by for a long time!