You can try to either subdivide your plane first (no smoothing algorithm) or give it some volume if it doesn't have one and see if that does the trick.
If the arrow is made out of two intersecting objects, you could bool them separately or bool them together first or model it cleanly to begin with (although the resulting outline looks clean).
If the resulting geometry is clean, you can also simply delete the inner faces of the arrow or connect one of its vertices with the border of the bigger mesh to maybe be able to delete it. Maybe the hole is already there, but some of the hidden edges of the bigger mesh need to be turned.
Or look into using Booleans with open meshes if that's what you are interested in doing. Can't remember the specifics or requirements. There is also an alternate Boolean Compound Object in Max.
The new Smart Extrude (edit/editable poly) might also be a way to do this without using Boolean.
