splitting a surface with curves

Hi everyone,

I am trying to split several surfaces with curves, after splitting I would like to remove some of the areas that resulted from the splitting, I have attached rhino file + a photo in which the areas I wish to delete are colored in yellow. 

I have tried to split the boundary of the surfaces using the intersection points (  intersection of the curves and the surfaces) but that did not work with me

thank you in advance !!