A cutting phase does not require higher repetition numbers
In many gyms it is still common to increase the number of repetitions while cutting. They think that in this way the fat is broken down and the muscle is better defined and shaped.
I have already stated above that it is not possible to change the shape of a muscle. Furthermore, it has been observed that the number of calories burned at higher reps is slightly increased with lower weight, but not nearly as much as previously thought. To more effectively get a better muscle definition and lose fat, you have to put your body in a caloric deficit. This can be done by either incorporating additional training, e.g. more cardio or more workouts, to increase the calories burned with a stable diet, or by more and more restricting the food supply, that is a fat loss diet.
However, the drastic increase in the repetition numbers also has another negative effect. If the musculature was built up primarily in the range of low to medium repetitions, then the proportion of the white muscle fibers (fast-twitch muscle fibers) was also trained and built up by the corresponding training. If the repetition range is drastically increased, the training leads to a shift towards the red muscle fibers (slow twitch fibers).
Now the following happens: the body no longer gets the full training stimulus for the already existing and trained white muscle fibers. As a result, the body begins to degrade them slowly. In return, the body tries to build up red muscle fibers through the new stimulus. But for this he lacks the necessary nutrient supply due to the negative caloric balance. The result is ultimately a loss of muscle mass.