With the latest patch bows do cut damage. In the game, arrows do not display a damage type. On the cRPG site, arrows display the damage type as piercing.
Do arrows do piercing damage on top of the bow's cut damage, or do they simply add (cut) damage? I believe that arrows add damage of the same type as the bow, not piercing damage. I do not think the game engine is coded to handle mixed damage types, nor do I have any reason to suspect it is capable of doing so.