Joining shapes together

I’m reading what you want in a different way…
I’m assuming that the red outline is the cutout of the part…?
If you want to engrave the black layer and cut the red layer, don’t join them
Run the black layer first, then the red to cut it out…
Might want to make that outline a bit larger than the engraving…
I assume you want something like this… Mickey is on a different layer than the cutout layer…