In a past post I created a box to mount a new medicine cabinet for a bathroom remodel. Naturally, I had to over cut the existing wallboard to do this build.
I then used pieces of new wallboard that were screwed into the existing structure using drywall screws. It is typical to custom cut the entire piece of drywall before it is install. That cut would include the hole for the medicine cabinet. However, there are risks doing this task that way. Most of those risks involve improperly measuring or cutting the hole. An alternative way is to use Dremel type tool with a drywall cutting bit. You simply cut into the center of opening and then move the bit to the outer wall and guide it along the edge against the framing. This is especially good when you have a small cut or an irregular one. It avoids any mistakes as you are cutting directly against border of the objet that you want to cut out.