A tomato is mainly water, but a sharp knife is needed to cut through it. A knife works by concentrating the force you apply downwards into the very narrow region of the blade tip. A knife blade is between 1 and 3 millimeters thick, but its sharp edge is much thinner, one thousand times thinner (1 to 3 microns) on a well sharpened knife.

When we first press a knife against food, the knife does not cut it, but instead squishes the food. The squishing before cutting is very evident when cutting tomatoes, but it happens even for stiff things like carrots. As one presses down the knife, the sharp edge and the food push harder against each other until at one point the food starts to break, which lets the knife edge advance into the food.

Imagine a block of jello (gelatin) being cut by a karate hand. If you press down just a bit, the jello will just give a bit, but if you increase the pressure your hand will start going through the jello.

Serrations help change the direction of squishing. When running over the surface of a tomato, the edge of the knife holds down the tomato while the serrations squish the tomato in the horizontal direction. With less volume to give and the edge of the knife preventing much movement it is easier to reach the stage where the sharp edges and the tomato are pushing hard against each other. Serrations also protect the sharp edge, help concentrate the cutting pressure, and give the edge extra rigidity. They also have one big disadvantage: they slow down cutting.

To visualize how serrations work, imagine the tips of your fingers are the teeth of a knife. If you spread them to form a rake and rub them horizontally over the block of jello, little pieces of jello will break off. If you imagine the jello as an inch thick sheet over a strawberry pudding, pressing down with a karate hand would do little to cut the concoction, but the rake hand has a chance. The sheet of jello over pudding is a bit like the skin of the tomato holding its soft innards.

I have found very little scientific literature on how knifes, including serrated knifes, work on food stuff. Any work you know of or have conducted, I would be curious to hear about.