Is it permissible, if one has food that will otherwise be spoiled, to tear plastic wrap and cover the food with it on Shabbos? I ask because in the case of plastic wrap, it’s not cut to an exact line (as opposed to toilet paper or paper towels which is). Would this be allowed, or would it still be considered tearing (or another issue like handling mutzkeh)?
As the article Gershon Gold in the comment section linked says, it is not allowed. See here. I was reading the article on my phone, before writing this article, and saw that it was already linked in the comments.
One is not allowed to tear Saran wrap (or other clinging plastic wraps) on Shabbat and even without the cutter. Using the cutter to cut the desired size would be even more severe since it would be a Torah prohibition.
The same principle applies as with tearing aluminium foil. See here.
Aluminum foil should not be ripped on shabbos, not L’chatcila and not b’dieved, and it must be pre-cut before shabbos. The reason is because ripping the foil is korayah, and also it is making the foil usable and considered makeh b’patish.
See also שמירת שבת כהלכתה.
The most notable difference between saran wrap and tin foil is that tin foil usually is put in a box with an cutting edge in the box itself. With saran wrap, however, it is not the case, you'll need to tear it directly off from the roll itself (in Europe in any case). Both methods are, according to the above, not allowed to be done on Shabbos, and should be done before Shabbos starts.
Refer to here:
There are 39 acts that are prohibited, one of them being Mehatech, or cutting for a creative purpose. If someone were to rip open a potato chip bag, for example, this would be permitted because the cutting is destructive in nature and because one is not doing so for the sake of cutting, but rather to access the food inside. If one cuts paper for a constructive purpose, however, the Mishna Berura (O.H. 340:41) explains that one would be liable for both acts of Kore’a (tearing) and Mechatech. Thus, cutting aluminum foil or plastic wrap is not permitted on Shabbat, and certainly not cutting precise sizes or shapes so as to properly cover food.