We are beginning Klal 36, which discusses the melacha of mechateich. One of steps to processing leather was cutting it to a specific size in order to use it. Thus, cutting the leather, or any other item, to a specific size is the melacha of mechateich.
The Chayei Adam writes that cutting any item which a person needs to a specific sized length or width, whether of wood, metal or even the tips of feathers (which the Gemara says were used as soft stuffing for a pillow) is chayav under the melacha of mechateich. This applies when the person wants a certain amount or size of the item, and when the cut is performed intentionally. Mechateich is different from many other melachos in that if the action is missing intention, it is not a davar she’eino miskavein, but it is not considered a melacha at all. Definitional to this melacha is the fact that the cut is a purposeful cut, so if it is lacking intention, it is not chayav at all.
Similarly, if one cuts an item for the purpose of destroying it, or to keep their hands busy, they are patur. Although the item is being cut, since it is not being cut for a functional purpose, it is not included in the issur deoraysa.
The Chayei Adam uses the language that the item in question is being cut to a “specific sized length or width”. The poskim discuss how specific the size must be in order to be included in the issur deoraysa. In the example of the Gemara of cutting feathers, the intention does not seem to be to have them at a specific measurement, but to only include the soft part of the feather. If so, Rav Falk and Rav Nissim Karelitz point out that cutting something to an approximate size would also be included in the issur of mechateich, if the cut is purposeful and fulfils its needed function.
We mentioned that there is no issur of korea to cut the twine holding together a bakery box. However, if one cut the twine at a specific place in order for the cut pieces to be of a specific size (eg, in order to use it in the future for something else), cutting the twine would fall under the issur of mechateich.
Summary
The melacha of mechateich is the issur of cutting something to a specific size. The cut must be made intentionally for the purpose of sizing the item for a functional use. It does not need to be a specific measurement, but even an approximate measurement will be chayav if it fulfills the needed function.