A rapid combustion process was introduced for the preparation of magnetic copper–cobalt ferrite, which was characterized using X-ray diffraction (XRD), vibrating sample magnetometer (VSM), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and Brunauer–Emmett–Teller techniques (BET). The prepared magnetic copper–cobalt ferrite showed a large specific surface area (104.6 cm2/g) and nanoscale particle size (55.4 nm), with a saturation magnetization of 19.6 Am2/kg. The nanoparticles were used to adsorb and remove Congo red (CR) from dyestuff wastewater, and the adsorption mechanism was revealed. Compared with the pseudo-first-order kinetic model and intraparticle diffusion kinetic model, the pseudo-second-order kinetic model was better at describing the CR adsorption process on the Cu0.5Co0.5Fe2O4 nanoparticles, while the Temkin isotherm best fitted the CR adherence on the Cu0.5Co0.5Fe2O4 nanoparticles. All data suggested that the adsorption of CR on the Cu0.5Co0.5Fe2O4 nanoparticles followed the mono-multilayer hybrid chemisorption mechanism. In addition, as the pH increased from 2 to 10, the adsorption capacity of the Cu0.5Co0.5Fe2O4 nanoparticles for CR decreased, indicating that an acidic environment was beneficial for the adsorption of CR on the Cu0.5Co0.5Fe2O4 nanoparticles. When recycling the Cu0.5Co0.5Fe2O4 nanoparticles after adsorbing CR, the relative adsorption rate was still 62.5% of the initial adsorption capacity after five cycles, revealing the reusability and promising applicability of Cu0.5Co0.5Fe2O4 nanoparticles in sewage treatment.