Natural fiber-reinforced composites (NFRCs) are a promising type of structural and functional materials. The problems are due to the limited data on the influence of the pneumomechanical processing on the quality of plant-based fibers to produce organomineral composites and due to the high energy consumption of this processing. The relevance of the problem stems from the expansion of the application field of plant fibers as a reinforcing filler of NFRCs and from the need to reduce energy consumption for processing fibrous materials. This study investigated an original transport and handling installation in the test processing of cotton cellulose sheets. The energy consumption of the mill during with impact fracture processing is 60 J/m. Experimental specimens of organomineral composites were fabricated using the processed plant-based fibers and gypsum. The filler concentration was 5% (wt.), and the water: gypsum ratio was 0.95:1.00. The specimens of these composites in compression were mechanically tested in compression on a universal tensile machine. The mechanical properties of the specimens of organomineral composites in compression were measured: ultimate strength σ = 3.0 MPa, longitudinal elasticity modulus E = 10.1 GPa, and relative elongation at failure ε = 2.6%. The pneumomechanical processing of plant fibers on the original installation leads to a 16% increase in the strength of the plant fiber/gypsum composites. The findings from this study can be applied to pneumomechanical processing of fibrous materials made of plant fibers. The processed plant fibers can be used as a reinforcing filler of organomineral composites, NFRCs, including functional composites with enhanced fire resistance.