Hi - as you have found out, mesh Booleans are not Rhino’s strongest side.
One work-around that you could try is to turn on the points of the mesh and then manually select the ones that are on one side of the trimming plane and simply delete those. Remember to copy the object in place and do the same with the points on the other side of the plane. There will be some work to do to create new triangles along the cut plane but at least it’s a way out…
If you upload the .obj file for your mesh I can try splitting it with my script which works much better than the Rhino Split Mesh command. Or if it is too big, you could post a link to it on Goggle Drive or something similar. Or send me a PM with the link if you want to limit access.
Your mesh is tiny compared to the 18M face mesh that I split with my script so it should have the capacity to deal with your mesh. But if your mesh has non-planar faces then this could be a problem.
This mesh has some issues. For the top half:
2156 pairs of faces that intersect each other
For the bottom half:
3953 pairs of faces that intersect each other
212 non-manifold edges
44 duplicate faces
All of these are in the starting mesh so none were added during the split operation.
The Rhino .3dm file with the split sphere is on Google Drive:
The split sphere is on layer Pieces. The starting mesh is on layer Start Mesh. The closed polyline used to split the sphere is on layer Ordinary. My script does not use cutting planes, it uses any number of closed polylines which can be straight or curved. For your case, I used a polyline with straight lines between the corner points.
The Python script is attached. It has an Eto GUI that works on Windows 10 and may work on Mac Rhino 6 WIP but not Rhino 5 as it does not support Eto I believe. To use the script, select Split on the first line of radio buttons, Reuse on the second line of radio buttons and then press the Split Mesh button. On my machine it splits the mesh in under 10 sec.