This study focuses on a comparison of alkali-activated materials based on natural zeolites without and with the addition of blast furnace slag and their subsequent modification by acid leaching. The addition of slag to alkali-activated mixtures is generally used to increase the strength. The subsequent modification of its chemical, textural and mechanical properties by acid leaching makes this material usable in other industries, especially in the chemical industry. This study aimed to examine the influence of the addition of blast furnace slag to alkali-activated mixtures based on natural zeolites and observe the effect of subsequent acid leaching on the chemical, textural and mechanical properties and CO2 adsorption capacity of these materials. The modification of alkali-activated materials was carried out by acid leaching using 0.1 M HCl and then using 3 M HCl. The properties of these materials were determined using N2 physisorption, Hg porosimetry, XRF, XRD, DRIFT, TGA and strength measurements. The results showed that the addition of blast furnace slag significantly increased the cutting-edge strength of the obtained materials and affected the textural properties, especially in leached samples. The presence of blast furnace slag generated a higher proportion of mesopores, which are attributed to the presence of the calcium silicate hydrate (C–S–H) phase and are easily removed by leaching, as shown by the XRF results. The obtained data showed an improvement in properties and extension of the potential applicability of these materials in the chemical industry, especially for catalytic and adsorption applications.