I heard back from support. The issue is that the clipping brushes don’t really “clip” like a pair of scissors or a knife. They’re really more of a collapsing brush. So if you want to cut a barbell in half lengthwise it won’t work as you might expect. You’ll end up with a flat profile of the clipped section of the barbell attached to the end.
I asked if there were another way to actually cut and delete portions of a model. This was their response:
"What you can do is this. Hide the portion of geometry you wish to delete. Then go the the Tool>Geometry Sub-Palette and click on Delete Hidden. Once you have done that then you can click on the Close Holes button next to the Delete Hidden.
Small note. You can not File Holes if the mesh has subdivision levels and before doing the Delete Hidden Mask your whole mesh the highest Subdivision level and then walk down to delete the geometry."
I would add that the “Delete Hidden” button is only available if your model has been converted to a Polymesh3D. The selection tools are available when you hold down Shift+Command. You can then choose from a variety of selection tools from the tool palette.
I hope this helps anyone having problems. Calling these brushes “Clipping” is the root of the confusion.