Portland cement is one of the most commonly used mineral binders in the Civil Engineering. Since the Portland cement production requires a large amount of energy, the process itself is burdened with a high greenhouse gas emission, primarily carbon dioxide, which has a significant impact on global warming. For a very long time, the scientific community has been investigating the application of different materials as substitute cement additives in production processes or even alternative to the cement as new mineral binder. All attempts actually lead to global sustainable development and the lowest possible impact of cement industry on the environment. The effect of the furnace slag from iron production industry as a substitute additive on the hydration kinetics in the system of paste as well as the values of developed compressive and flexural strength in the system of the cement mortar was determined by using the slag as a substitute additive on CEM I 42.5R where the cement mass has been replaced with slag in the amounts of 5, 15, 20, 25, 30 and 40 mass % by weight. One mortar serie was made with the cement type CEM II B-S 42.5N prepared in the laboratory. Samples of the cements mortar were kept in the thermostated water until the measurements of developed compressive and flexural strengths were performed after 3, 7, 14, 28, 70 and 90 days of hydration. The results show that after 90 days of hydration, even the system with 40 mass % of slag shows higher value of developed compressive strength relative to the reference mortar (mortar without replacement slag). The measurements also confirm that there are no significant deviations in the values of the developed mechanical properties of cement CEM II B-S 42.5N compared to the mortar systems were slag was used as a substitute additive in CEM I 42.5R cements systems. The results of the kinetic analysis showed a slight decrease in the value of the nucleation and growth rate constant, while on the other hand, it significantly influenced the duration of the process itself by moving it towards higher hydration times. The shift of nucleation and growth to later times results in a higher degree of hydration of the cement clinker minerals, which influences the mechanical properties observed in the mortar systems, but also the earlier appearance of the period in which the diffusion is a limiting hydration process as a consequence of increasing of the microstructural density of the hydration products in earlier hydration period.