Sharpeners are used to cut a sharp point on a blunt pencil.
Standard sharpeners won’t work on a carpenter’s pencil because of the pencil’s rectangular or oval shape.
There are, however, sharpeners that are specially designed for carpenter’s pencils.
Because of their rotational sharpening, these sharpeners can only make a conical point on a pencil. For more information on the different types of point, see: What are the different types of pencil tip?
If you want a tip other than a sharp-pointed conical one, then you will need to use a knife.