I removed the upward face to the side (which is weird to have) I exploded your original shape and made a new network surface, I made 100% sure that it would cut through the edges of the surrounding surface by using surfextend on the edges. I used UNION to stick the extensions and the original surface together then the slice worked fine.
It was either the upward side causing an issue, or your cutting surface did not cross the vertical surface completely.
These kind of operations will go smoother if you use solids instead.
Design a solid shape and use a surface to cut off the top/bottom of your solid.
