(1) Background: A comparative research study to remove Congo Red (CR) and Methyl Orange (MO) from single and binary solutions by adsorption onto cobalt ferrite (CoFe2O4) and cobalt ferrite–chitosan composite (CoFe2O4-Chit) prepared by a simple coprecipitation method has been performed. (2) Methods: Structural, textural, morphology, and magnetic properties of the obtained magnetic materials were examined by X-ray diffraction (XRD), Fourier-transform infrared (FTIR) spectroscopy, N2 adsorption–desorption analysis, Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), and magnetic measurements. The optimal operating conditions of the CR and MO removal processes were established in batch experiments. The mathematical models used to describe the processes at equilibrium were Freundlich and Langmuir adsorption isotherms. (3) Results: Cobalt ferrite–chitosan composite has a lower specific surface area (SBET) and consequently a lower adsorption capacity than cobalt ferrite. CoFe2O4 and CoFe2O4–Chit particles exhibited a superparamagnetic behavior which enabled their efficient magnetic separation after the adsorption process. The research indicates that CR and MO adsorption onto prepared magnetic materials takes place as monolayer onto a homogeneous surface. According to Langmuir isotherm model that best fits the experimental data, the maximum CR/MO adsorption capacity is 162.68/94.46 mg/g for CoFe2O4 and 15.60/66.18 mg/g for CoFe2O4–Chit in single solutions. The results of the kinetics study revealed that in single-component solutions, both pseudo-first-order and pseudo-second-order kinetics models represent well the adsorption process of CR/MO on both magnetic adsorbents. In binary solutions, adsorption of CR/MO on CoFe2O4 better follows the pseudo-second-order kinetics model, while the kinetic of CR/MO adsorption on CoFe2O4–Chit is similar to that of the dyes in single-component solutions. Acetone and ethanol were successfully used as desorbing agents. (4) Conclusions: Our study revealed that CoFe2O4 and CoFe2O4–Chit particles are good candidates for dye-contaminated wastewater remediation.