The binding potential of fly ash (FA) as a typical basic component of building mixtures can be improved in mechanical way, which unfolds new possibilities of its utilization. This paper presents the possibilities of preparing the geopolymer mixtures based on ground (d m = 31.0 µm) FA, used in varying percentages to the original (unground; d m = 74.1 µm) one. As a modification, fine-grain sludge from the process of washing the crushed aggregates was used as filler in order to obtain mortar-type material. The basic physical-mechanical properties of mixtures are presented and discussed in the paper, focusing on time dependence. The following standard tests were executed after 2, 7, 28, and 120 days: density, total water absorption, flexural strength, and compressive strength. Ground FA provided for positive effect in all tested parameters, while incorporation of fine portion of sludge into the geopolymer mixture does not offer a significant technical profit. On the other hand, it does not cause the decline in the properties, so the environmental effect (reduction of environmental burden) can be applied through its incorporation into the geopolymer mixtures.