Extruding / wire cutting out material on a curved surface of a solid

Trying to cut/extrude a curved profile into a 3d object.

I have projected the cut lines onto object surface but can not get matteral removed. Trying to cut a small rabbit or trough in this geometry. The green line needs to be extruded into gray object removing the material.


Draw the profile for the cut and then use Sweep1 or ExtrudeCrvAlongCrv to make the trough surfaces and then trim / split and join.