The choice of a proper knife to cut hard cheeses depends on the type of dough and its hardness. Often hard cheeses can not be cut in slices because of their grainy texture (just think of Parmigiano or Grana). In order to make portions, you need a Parmesan almond-shaped knife, ideal to detach even the flakes with an irregular shape.
You can use either smooth or serrated blade, and even a hook knife to cut the rind before the actual cutting can be helpful.
To make Parmigiano flakes, you can comfortably use a truffle shaver.