The study is devoted to assessing the possibility of replacing natural gypsum-anhydrite stone with man-made fluorogypsum waste (gypsum dihydrate and anhydrite) as a calcium sulfate additive in the production of Portland cement in compliance with environmental standards. It was found that such a replacement is technically feasible, but requires taking into account the specifics of the waste: when anhydrite is heated in the range of 320–450°C, hydrogen fluoride is released, which emphasizes the need to control the temperature conditions of processing. The kinetics of strength gain of cement-sand samples manufactured according to GOST 30744-2001 is successfully described using the Avrami-Erofeev equation (the proportion of explained variance ≥0.99). It is shown that the composition with fluorogypsum dihydrate slows down the growth of strength at the early stages of hardening, while the addition of anhydrite increases it in the initial period. This is due to the slow release of sulfate ions (SO₄²⁻) from anhydrite, which suppresses the premature formation of ettringite and stimulates the hydration of silicate phases. Replacing natural gypsum with technogenic gypsum increases the setting time of cement and causes a slight decrease in compressive and flexural strength due to differences in the kinetics of new formations and the hydraulic activity of technogenic components. The results confirm the technological feasibility of using fluorogypsum waste in the cement industry. The work contributes to solving the problem of recycling technogenic waste and reducing resource costs in the construction industry.