Clip paths are like a transparent masking applied to an image to hide parts of it. (Say you’ve got a square picture, and you only want to cut out the picture inside of an oval shape - you can overlay an oval clipping path and all of the data outside of the oval is hidden.)
The problem is, they don’t really get rid of the data, they just hide it. The Glowforge interface can still see the hidden data.
You need to completely remove the hidden areas, not just hide them. You can do that using the subtraction tools in either Illustrator or Inkscape.
For instance, in Illustrator create the clipping mask and then in the Pathfinder pallette, click on “trim”, expand it and then ungroup. This will trim the excess outside of the clipping mask.
(There might be other ways to deal with it as well…that’s the one I’m familiar with.) 