Splitting a Surface by Another Surface
- 
                Select Intersect > Combine
                    
.
             - Click the surface you want to cut.
 - Click the surface you want to cut the surface with.
You can Ctrl+click multiple surfaces that together completely intersect the target surface to fully cut the surface. You can box-select surfaces that only partially intersect the target surface to partially cut the surface.  - Mouse over the surface to see the regions created by the cut.
 - Click the region you want to delete.