Split surface problems

I am having problems to cur the surface (red) with the plane (green) I am really new with grasshopper and everything is a little dificult, pls can anyne help me.
Thank you in anticipation

test_1.3dm (362.7 KB) test_1.gh (24.5 KB)

How about something like this:
test_1_v2.gh (23.4 KB)

That is absolutly fantastic, just one more requierement if it is posible. I would need to have them in two diferent “files” so I can continue working with them independently. Is that possible??

Thank you very mucho Adam for that fantastic work

Not sure I follow. You mean the two halves in two separate GH files? If so, look at Data Input/Data Output.

I mean to divide it in two diferent output but in grashopper so I can work in grasshopper individualy with both halves. like two differents chanels

everything solve thank you very much

If you use list item, and zoom in on the component you can click plus get the different items.