Let me introduce the "Bisect" modifier.
Although I`m not a programmer, I hope you may find my proposal useful and not too horribly done.
It cuts geometry by plane removing the other half. Actually, it works similar to the "Mirror" modifier with the "bisect" option switch on. Except, it doesn't create mirrored half.
The code is very close to "Mirror" modifier, I`m sure it might be optimized furthermore.
I`d like to add the option to close cut with polygons the same way as it works in mesh editing mode.
Here how it works:
Also, I designed icon but hadn't managed to add it properly to the blender_icons.svg
P.S. Please, dont throw stones at me if I made something wrong or violated the submission procedure.