cut perpendicular to surface

Hi There,

I am trying to make a cut that is perpendicular to the surface.  Note that there is a not a single "direction" for this to work.  I looked at using wrap or "thickened cut" but can't get these to work.  Do you have suggestions for how to most directly do this?  Attached part with outline/surface of where the perpendicular cut need to occur. 

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