There has been much speculation as to the purpose of the sawfish’s saw.  Speculation was

There has been much speculation as to the purpose of the sawfish’s saw.  Speculation was that they were used to literally saw chunks of meat from large prey such as whales or dolphins.  In fact, the saw is lined with thousands of sensory organs that allow the sawfish to detect the electric fields emitted by living creatures, thus helping them track prey.  Once a fish is detected, the sawfish will strike the prey with a sideways slash of the saw, stunning it, or else use the saw to pin it to the sea floor.  While the saw is not used specifically to cut prey, a fish may be sliced in half by a particularly vigorous swipe.  The saw is also used to defend the sawfish against large predators such as sharks, or in battles with rivals.  

In contrast to stories of sawfish cutting through the bottom of boats or sawing humans in half, sawfish are known to be docile and harmless animals when left undisturbed.