In modern concrete technology, the use of various types of additives and admixtures is standard. They not only affect the mechanical properties of cement composites but also significantly facilitate the formation of a concrete mix. The paper presents the effect of the content of silica fume (SF) and an amorphous aluminum silicate (AAS) on selected properties of cement mortars, such as flexural and compressive strength, water absorption, freeze–thaw resistance, and shrinkage. The dynamics of strength development, determined after 7, 28, and 90 days of maturing of test samples, are also presented in the paper. Mortars modified with the addition of amorphous aluminum silicate in amounts of 5% and 10% of the cement mass exhibited increased flexural strength within the range of 25–30% in comparison with standard mortar and mortar modified with the addition of SF of the same amount. In the case of compressive strength, both additives resulted in similar increases in the strength within the whole maturation period. The freeze–thaw resistance tests showed that the mortars with the addition of AAS were the most resistant to variable freezing and thawing cycles, in relation both to the control mortar and to the mortar modified by SF. The application of AAS resulted in a significant reduction of shrinkage strain (by more than twice) in comparison with mortars prepared with the analogous amount of silica fume.