Does ZBrush have a brush that cuts absolutely everything under the cursor, creating a through hole?
For cutting through the mesh in order to cut a chunk of it off, the Trim or Slice brushes can work. These will only work on a single subtool at a time, and if you attempt to create a hole / tunnel then you may have to manually remove some faces and bridge the two holes together.
Personally I would use a boolean over a brush for this. You’ll get the holes and tunnel automatically, can adjust it around as needed, and can use it to affect multiple subtools.