Nowadays, global warming and the ensuing climate change are one of the biggest problems for humanity, but environmental pollution and the low ratio of waste management and recycling are not negligible issues, either. By producing alkali-activated cements (AACs), it is possible to find an alternative way to handle the above-mentioned environmental problems. First, with a view to optimizing experimental parameters, metakaolin-based AACs were prepared, and in it, waste tire rubber was used as sand replacement (5–45 wt %). Insufficient wetting between the rubber particles and the matrix was corrected through different surface treatments of the rubber. For improving the mechanical/strength properties of the specimens, fibrous waste kaolin wool (0.5–1.5 wt %) was added to the AAC matrix. Considering the results of model experiments with metakaolin, blast-furnace-slag-based AAC composites were developed. The effects of storage conditions, specimen size and cyclic loading on the compressive strength were investigated, and the resulting figures were compared with the relevant values of classic binders. The strength (44.0 MPa) of the waste-based AAC composite significantly exceeds the required value (32.5 MPa) of clinker saving slag cement. Furthermore, following cyclic compressive loading, the residual strength of the waste-based AAC composite shows a slight increase rather than a decrease.