If you want to cut up a scene then you'd first need a clear definition of what constitutes a scene. The most common definition of a scene is that it’s a unit of a story that takes place at a specific location and time. If either the location or time would change, then this would mean that there would be a new scene. Unfortunately there’s no clear cut answer to your question. How you’d split the scene would depend on several factors. Since I don’t know the specifics I can’t give you a straight answer, but I can offer you a framework to figure out what questions you need to answer. (It will be broad but it might be useful).
First off, is the comedy you’re writing multi cam or single cam? Multi-cam means it’s like the Big Bang Theory, The Brady Bunch or any other similar sort of sitcom. These shows are often shot on stages. Scenes here are often built in the same way you’d construct a mise en place in the theater, there’s a unity of time and location. Jokes often have quick pay-offs and are contained in one area. This means that you can chain locations easily through the use of your loglines if these stages are connected. So INT. Living Room INT. Kitchen etc. To imply quick cuts you could use O.C and O.S to have characters interact while in connected spaces. Quick hard cuts are not often seen in this format unless for comedic effect.
Try to think of your scene as a series of interconnected actions that lead to a singular pay-off that leads into a new series of sequences.
If you’re writing a single cam comedy, then you can be a bit more liberal with your cuts in general. A single cam would be something like It’s Always Sunny in Philadelphia. Just figure out a what the emotional arc is that the characters throughout the sequence you’re creating and you’ll be good to go. You can use CUT TO if you like, or simply use a log line to switch between locations.