In SpaceClaim there are two approaches.
One is to use the Facet tab to convert the solid into a Facet Body, use the tools on the Facet tab to split the Facet body, then convert the Facet body back to a solid.
Another is to convert the solid to a facet body, but then use the Auto-Skin tool to create a much simpler surface geometry that will easily be split and much easier to mesh.