The trend in building materials science is to replace the different proportions of Portland cement in the binder. Therefore, the paper proposes the principles of controlling the static and dynamic strength of fiber-reinforced concrete, consisting in the complex effect of the hydro-removed ash and slag mix and basalt fiber on the processes of structure formation of the cement composite. A four-stage purification system for the hydro-removed ash and slag mixture has been developed, including disintegration, flotation and two-stage magnetic separation. It was found that the density of the fresh mix from the dose behaves naturally, and the density of solid samples at low doses slightly decreases. High early strength of the developed composites is noted, in particular, for specimens with ASM, one and a half increase in compressive strength is traced in comparison with non-additive specimens. Combinations of "fiber + ASM" with a quadrupling of strength have a significant effect on bending strength. Successful approximations of the compressive strength and bending strength on the ASM dose for different ages (1, 7, 28 days) are traced with the regular behavior of the coefficients in the power dependences. Revealed a multiple increase in the impact strength of the developed compositions. The use of the results will lead to the possibility of designing high-strength concretes, including for special structures.