From Rebirth of the Night Wiki

The Saw is a mechanical block that is used for cutting blocks into smaller pieces. It takes continuous mechanical power (not hand crank) from any side other than the blade. When powered and a block with a recipe is in front of it the block will drop into the items from the recipe.

The major usage of the saw for the creation of Minimized Wood.

Additionally the Saw is very sharp and is able to quickly dispose of mobs. Mobs that die between a Saw and the Chopping Block will have a higher chance to be behead.[1]