...
Note: Don't worry if the advance bar show more than 100%, this is because the final number of surfaces to be intersected grown because when a cutted surface is splitted the new surfaces are added to the collection to find more intersections.
If everything end successfully all surfaces will be divided. Some intersection could not be done because of tolerances (too small cuts, etc), and some manual extra operation could be required.
Now we can delete the unwanted part, e.g. to have only a volume of terrain under the rectangle for some geotechnical simulation.
Delete the unneeded surfaces.
Geometry->Delete->Surfaces
In the contextual menu click LowerEntities (to delete also its dependent lines and points)
and select the surfaces
Then the model must have only the surfaces that enclose a volume ,create it with
Geometry->Create->Volume->By contour
and select all surfaces
Final volume and detail of cutted surfaces