The increased early hydration rate of high early strength cement has economic advantages in many civil engineering fields (faster formwork removal or earlier demoulding of precast elements). Styrene–butadiene rubber (SBR) latex is the most common polymer in aqueous dispersions suitable for admixing in cement-based materials. It allows the designing of structures with specific properties for a variety of applications. The analysis of literature sources has shown that different properties of SBR latex-modified cement-based material samples reported were usually measured at 3, 7, 14, and 28 days of hardening. In this research, the authors decided to investigate a combined effect of high early strength Portland cement, characterized by an increased hydration rate, and SBR latex able to retard this process for a prolonged hardening period—up to 90 days in modified mortar samples. This study covers the results of the effect of different amounts of SBR latex (5%, 10%, 15%, and 20%) on the properties of modified mortar samples with a constant water-to-cement ratio prepared with high early strength Portland cement 42.5 R. The mortar samples were prepared from local raw materials produced by the Lithuanian companies. The properties, such as dry bulk density, ultrasonic pulse velocity, capillary water absorption, compressive and flexural strengths, and toughness, after three different hardening periods (7, 28, and 90 days) of the mortar samples were investigated. The applied mathematical–statistical methods allowed a detailed prognosis of the dependence between the dry bulk density and the strength properties of modified mortar samples. The combination of 42.5 R strength class Portland cement with the SBR latex in amounts ranging from 5% to 20% seems to be suitable for designing durable structures with specific properties.