How do I cut out a piece of a layer mask?

Thanks JJ and Dave! I like having different approaches based on the circumstances - very helpful!

If you are using the pen tool, you can use path operations in the options bar to control how the new path element you are drawing intersects with the existing path elements. So for your example choose subtract front shape

The same applies if you have made a vector mask from the path and are editing it.

If you have made a normal pixel mask then brushing with white makes the layer visible and black makes it transparent

Dave

You do not you paint with Black and White in the Layer mask to changed what they mask.  Black hides white shows.

So click the add layer mask icon in the layers palette that will add an all white layer mask to the layer. The layer mask will become the photoshop target Paint in the area you want to hide so the gold will show through the layer.