What does one use a saw for?
Any Kitchen I worked in –that does a bit of butchering– has one (any butcher also). It's for sawing bones.

At the time you would not throw anything out of an animal, and a lot of people would make their stock or put a piece of bone in a stew or soup for taste. But, as far as I know, they usually look like a hacksaw not like a the one you're showing. 

Maybe the illustrator did not know what a kitchen saw looked like. He's been asked to draw one and did a hand saw by mistake. 

This type of saw could be also used in a pastry shop. At some stage (and still, apparently according to @divi) wedding and other momumental cakes, but also smaller ones, were consolidated with pieces of wood or other non comestible material.