We are beginning siman 3. The Chayei Adam writes, based on the Shulchan Aruch, that the concept of mechateich does not apply to food. Thus, if a person wants to cut a piece of cake to a certain size, or divide a pie into exact slices, the melacha of mechateich does not apply. The reason it does not apply is because it is consumed shortly thereafter, so the action of mechateich does not have chashivus as a melacha. Therefore, if the food is meant to function as a kli rather than as food, the concept of mechateich will apply. For example, if one cuts branches in order to feed their animals leaves, the food is the leaves and not the branches. Therefore the concept of melacha will apply to the branches, even if it does not apply to the leaves.
The Chayei Adam continues, and points out that mechateich can apply to the food itself, if the food is being used as a kli. For example, if one uses the food to fix a kli, such as a hole in a kli which can be plugged with a carrot. Cutting the carrot to the specific size of the hole, albeit the carrot is edible, would be chayav for the melacha of mechateich. Another example would be using bread to plug the hole. When the hole is fixed through the placement of the food, the person also transgresses the issur of tikkun kli.
Similarly, the heter for cutting food does not apply to sculpting the food into an artistic shape which falls under the melacha of koseiv. Making general shapes, such as circles or triangles, is not a problem.
Summary
The concept of mechateich does not apply to food. However, it does apply to secondary elements of the food (eg, the branch to which the leaves are attached), or food being used as a kli.