WARNING: This page is about a different car, the 2003 GMC Sonoma, 2003 GMC Jimmy, 2003 Chevrolet S10 Pickup, and 2003 Chevrolet Blazer. However, it is still accessible from the selected car via links, so may be relevant.
Press the retaining tab under the cupholder while pulling outward in order to remove the cupholder from the bracket.