HowTo clip the mesh in paraFoam
From OpenFOAMWiki
The intuitive way to clip the mesh in paraFoam is using the clip filter. However this creates a flat, triangulated surface hiding the mesh's structure.
A more useful "clip" can be obtained using Extract Selection-Filter. The selection is created using the "Select Cells through" button
and pressing "Copy Active Selection" in the Extract Selection-Filter's object inspector.