It depends on which American Express card you use. For example, with the Blue, Blue Cash, Blue Sky, and Clear cards you do not have to pay off the entire balance every month. While traditional charge cards from American Express such as the Green, Gold, and Platinum must be paid in full every month.his Site Might Help You. RE: do you have to pay off your balance every month with an american express card? If you have an (any) american express credit card do you have to pay your balance off every month?