A saw is a tool used in carpentry.
Its primary purpose is to convert raw logs into usable planks. Its secondary purpose is to turn regular shotguns into the improved sawn off shotgun. The saw can also be used to cut watermelons into watermelon slices. Saws are also used in disassembling a lot of furniture, to get more planks and nails as well as leveling the player's carpentry skill. Saws have no durability so one can be used infinitely.
Saws can often be found in storage crates (which are typically found in warehouses). They can also be rarely found in some residential homes. The hardware store in West Point, KY is an excellent place to get a saw and many other useful tools relatively early in the game.
From items.txt (Project Zomboid directory/media/scripts/)
Weight = 0.7,
Type = Normal,
DisplayName = Saw,
Icon = Hacksaw,
MetalValue = 35,
StaticModel = Hacksaw,
SurvivalGear = TRUE,
Tags = Saw,
WorldStaticModel = HacksawGround,