The Standard Cart Summary Portlet really does not display the discounted price once a Promo Code or Gift Certificate is applied to the order. The Website Theme's Cart Summary Portlet code needs to be customized by adding in a website tag in order to reflect the updated price with the applied discount.
1. Navigate to Setup > Site Builder> Themes.
2. Click the Edit link next to the current theme being used in the webstore.
3. Navigate to the Sidebars tab.
4. In the Cart Summary Template field, customize the code and enter the Website Tag that will display the total discounted amount of the order:
5. Click Save.