Physics applied to parts of mesh

I am creating a cooking 3d game and designing models for it and I am wondering what is the best approach to create cutting food effect.
Is it better to create one original mesh and then it's cut parts that will appear on a screen or maybe designing 1 mesh with child and applying some kind of physics to it so for example when knife hits it it breaks?
I dont need extremely precise cutting animation as it will be a low poly game.
Any ideas welcome!

Is it important to you that the player's knife position corelates to the place(s) the food objects get cut? If so, I would look at some inexpensive "mesh slicer" scripts on the Asset Store. If not, I would suggest you just have three or four separate meshes that describe various stages of being cut up (whole, chopped once, chopped a few times, fully chopped up). The former is what games like Fruit Ninja would do, and the latter is what games like Overcooked would do.