Scrap tires have become one of the most serious environmental issues worldwide in recent years. Exploiting this scrap has caught the attention of researchers in their efforts to conserve the environment. From a structural engineering materials perspective, a partial fine aggregate in cement mortar can be replaced by crumb rubber produced from scrap tires. This research mainly emphasizes the role of adding 0.1% edge-oxidized graphene oxide EOGO (by the weight of cement) in enhancing the properties of cement mortars containing 5%, 10%, and 15% of crumb rubber (by sand replacement). Cube and prism specimens were employed to investigate compressive and flexural strengths at 7- and 28-day curing ages. A porosity test was also conducted after 28 days of curing. In addition, a scanning electron microscopy (SEM) test was performed to investigate the effect of incorporating EOGO on the interfacial transition zone (ITZ). Results showed an enhancement of the mechanical properties of cement mortar, including compressive and flexural strengths, with the inclusion of EOGO in the mixes. The findings demonstrated that adding EOGO can improve the mechanical properties of mixes containing crumb rubber particles. Specifically, the mortar mix with 0.1% EOGO and 5% crumb rubber exhibited better performance compared with the virgin mix without rubber particles. Therefore, crumb rubber is viable for use as a sand replacement when EOGO is included.