Saws are able to make cuts straight cuts (or grooves) into a material because all saws have a kerf.....This means, the width of the cutting teeth are either equal to or greater than the thickness of the blade, allowing the blade to follow the teeth down through the cut without binding. You can readily see the kerf on the wood saw of your SAK or Leatherman tool. In general, offset teeth which cut with their points, are more efficient for cutting wood and rows of parallel teeth work more efficiently for a metal saw. The blade of a hacksaw has side-to-side ripples down its length to create a kerf wider than the thickness of the blade so as to inhibit binding in the harder metals.
Normally saws are used to cut grooves and files are used on the surface of materials. Both cut with teeth which need to be pushed against the material as well as pulled or pushed. Some work both ways, depending on the set of the teeth.
Most heat produced in sawing or filing (or drilling) represents wasted effort. When sawing hard metals, sharp teeth and the use of a good lubricant speed up sawing, lessen effort and reduce the buildup of heat. When sawing wood or filing, sharp teeth reduce effort and the production of heat.
Knives have cutting teeth too but knives have no kerf. Their shapes come in variations of a wedge. They work by sawing, pushing material aside, or a combination. Push cuts (steady force) and chops (percussion) get the cut started with the thin edge and then wedge the material apart. Push cuts usually work best on thin materials or near the surface as when one sharpens a stick. Draw cuts use the teeth in a sawing action. If one attempted to use a knife to saw a thick, hard material like an oak branch, it would shortly bind in the cut because the intial cut, made by the edge, cannot accommidate the progressively thicker wedge of the blade. This is just as true in the case of a serrated knife blade.
In general, knives work better on softer materials and saws and files on harder materials although their is some overlap. A knife cannot cut a neat groove through a thick piece of wood (Although you could conceivably baton through it or gnaw through it with dint of much hard labor) and a saw or file would be inefficient in whittling a tent stake, compared to a sharp knife. There are endless examples.
BTW, molecules, which are combinations of elemental atoms, held together with electromagnetic force, are so small, that their destruction or formation is in the realm chemical reaction and not tools or cutlery, which work on much larger particles consisting of molecules (e.g. wood) or atoms (e.g. iron).