As noted that vector version of the SAC shield should cut well as a V carving:
It doesn’t lend itself to cutting different elements at different depths because a single piece of geometry:
will describe the outlines of multiple elements of the design
You would want a colour version:
if only it were drawn so that each element when selected would have an outline which would describe only the visual area of it — which is not the case:
For a bit on fixing this sort of thing see:
Basically, you’ll need to duplicate all of the overlapping elements and use either Trim Vectors, or Boolean Subtraction to arrive at geometry which describes only the visual portion of each element in a way amenable to how you wish to cut the design.