An important project is taking a toll on my mental health, I can barely control my emotions. How do I know if I should quit?

It depends do u like the job ur doing or are u doing it for other reasons. If you are doing it for other reasons and it is badly effecting your health than its time that you leave. There should always be a low when it comes to work but there should also be a high. If you don't see the high for a long time, then maybe its the time for you to leave.

It depends on the nature of the project but I would recommend you don't quit. I would recommend that you try and find a balance between your project and your mental health. Don't allow your mental health to take a back seat. Recognize what you feeling and accommodate those feelings. If you feel exhausted, take a break. If you feel mentally/emotionally exhausted, do activities that you enjoy until you feel ready to take on your project again. Don't quit. If you quit when something gets too tough you may find that you may not complete projects/activities in the future. Rather find your balance and persevere! Believe in yourself, and also give yourself a break.