Is zakat due on the original amount upon which a year has passed, or on the accumulated saved amount that has become a total after the zakat?

You are not obligated to pay Zakat on the money gained from your salary unless a complete lunar year (Hawl) has passed over it. It is permissible to assign a separate Hawl for each amount. However, the easier and better approach is to pay Zakat on all your money along with the Zakat of the first sum when its Hawl is completed.