To reduce the cost of epoxy asphalt mixture (EAM) pavement and increase the performance of mixture with high reclaimed asphalt pavement (RAP) content, three different dry-method styrene-butadiene-styrene (SBS) modifiers and an epoxy polymer (EP) were employed in this study to enhance the properties of aged asphalt binder and prepare SBS-modified epoxy reclaimed asphalt (SERA) binders. The chemical interaction between the dry-method SBS and EP was analyzed, and the microscopic structure and mechanical properties of the SERA binder were evaluated. Additionally, a discussion on the initial material cost of the newly proposed SERA mixture (SERAM) was conducted. Results indicated that the degraded products generated by the oxidization of dry-method SBS undergo interactive reactions with the epoxy rings present on the epoxy resin molecules. Phase separation occurred both between EP and SBS-containing aged asphalt binder, and between SBS and aged asphalt binder. The addition of dry-method SBS to epoxy reclaimed asphalt (ERA) increased the size of the asphalt binder phase in the fluorescence images. At EP contents ranging from 30% to 50%, the incorporation of dry-method SBS led to notable improvements in the elongation at peak, low-temperature properties, and fatigue resistance of ERA binder. The SERA binder exhibited comparable or even superior properties in terms of tensile strength, low-temperature behavior, and fatigue properties when compared to virgin epoxy asphalt (EA) binder. However, dry-method SBS may have a negative impact on the high-temperature properties and curing time of the binder. Dry-method SBS with rejuvenation capacity exhibited the greatest improvement in elongation at peak, low-temperature properties, and fatigue properties of ERA. Compared to EAM, the utilization of SERAM results in material cost-savings of approximately 46 USD (9%) per ton of mixture.