Intersect Mesh and keep faces colours

Hello everyone,

Is there a way to execute a mesh intersection and keep the original colour to the mesh’s faces?
In the image below you can see I have a coloured white and green mesh, and I want it to be cut by the red line, which is closed (could be transformed into another mesh or surface). the mesh is open but I could turn it into a solid if necessary.

The meshes represent tiles on a facade, like so:

and they need to be cut in the places where there are windows/doors or the facade is over.
I am using grasshopper to map the tiles to the facade.

Thank you all!