‘Cut it out’ is used in cases where you want the person to stop something completely. It still can work, but it would be advocating for them to stop the activity completely.
‘You need to cut it out on the workouts - otherwise you'll damage your muscles (or: you'll hurt yourself).’ I left out the workout part as it would be assumed from context. In this case, ‘take it easy on the workouts’ is probably better than ‘cut it out,’ as they probably just need to reduce their exercise intensity rather than stop it entirely.
‘Cut it out with the TV - it's too loud!’ This is more simplified and natural sounding. It'd be obvious from context that you were being bothered/disturbed. If you just wanted them to turn it down, you could say: ‘Turn it down - that TV's too loud.’