Designing adsorbent materials that can effectively remove many types of organic dyes is crucial because of the wide diversity of synthetic dyes found in wastewater. Thus, this study presents the synthesis of economic and eco-friendly adsorbent composites composed of chitosan (Cs), talc (T), and Cloisite 30B clay (C) to remove both cationic crystal violet (CV) and anionic reactive yellow 145 (RY) dyes for the first time. Cs was functionalized with T and subsequently the CsTC1 and CsTC2 composites were prepared by sensitizing the obtained CsT with different weight ratios of Cloisite 30B (C). X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy (SEM), thermogravimetric analysis (TGA), N2 adsorption–desorption isotherm, and zeta potential analysis were employed to characterize the materials. The addition of T to Cs matrix improves the thermal stability, pore size, and pore volume with respect to pure Cs. The effect of C inclusion was examined by measuring the affinity of the prepared composites towards adsorption of cationic CV and anionic RY dyes in comparison to pure Cs and CsT composite. The adsorption results in a single dye solution revealed that the CsTC1 composite is the most effective adsorbent for removal of RY dye with 76.9 mg/g adsorption capacity, whereas the CsTC2 composite exhibited the highest adsorption activity for CV dye (37.03 mg/g). Furthermore, RY and CV co-adsorption on CsTC composites was tested from a mixed dye solution. The adsorption kinetics of RY and CV adsorption followed the pseudo second order model. Langmuir isotherm model described the experimental adsorption data better than the Freundlich, Dubinin–Radushkevich, and Temkin isotherm models, indicating a monolayer sorption process for both dyes. The proposed mechanism for RY and CV adsorption using CsTC composites was investigated.