Currently the global trend is to expand the range of construction materials produced using resource-saving technologies that do not generate CO2 emissions. An important role in this is given to gypsum-anhydrite binders and concretes which can be obtained using a non-burning technology with the involvement of technogenic wastes which excludes the emission of carbon dioxide into the environment in comparison with Portland cement technology. The article is devoted to the results of studies on obtaining anhydrite binder from the by-product of sulfuric acid decomposition of fluorite concentrate – fluorine-anhydrite using other by-products of industry (metallurgical, mining and heat power) acting as active mineral additives. The influence patterns of such additives composition and quantity on the kinetics of milling and neutralization of fluorine-anhydrite are established. It is shown that the milling capacity of the anhydrite binder depends on the degree of binding of the acid component as well as the stoichiometry of chemical reactions between sulfuric acid contained in fluorine-anhydrite and additives minerals. The process of the acid component binding proceeds most actively with the addition of steel-refining slag in an amount of 12.3 % which allows to achieve a high milling rate of the binder. The resulting products of neutralization reactions are centers of crystallization which increases the hydraulic activity of fluorine-anhydrite. As a result, anhydrite binder comparable to Portland cement by physical and mechanical properties have been obtained. This binder is suitable for producing high-strength concrete of B30 class in which granules from neutralized fluorine-anhydrite are used as a coarse aggregate. Thus, the study made an important contribution to the material science of technogenic materials expanding their use in construction.