You could say "je pars du travail", meaning "I'm leaving from work". The situation is a bit muddled when using "quitter".
Je quitte mon travail. -- I'm quitting my job. Without context and in general, this means that you are actually terminating your job and no longer work there. To be even more explicit, you can say "je quitte mon emploi".
Je quitte le travail. -- I'm leaving work. This is usually understood as you are leaving from work and not as terminating your employment.