Clay-salt slimes, production wastes from "Belaruskali" (A Belarusian factory, producing potash fertilizers), have been tested as a low-cost, eco-friendly potential sorbent for the removal of radionuclides from aqueous solutions, and may be a component of the cement filling of drums used in the storage of radioactive wastes. The efficiency of sorptive removal of caesium(I)-137, strontium(II)-90, europium(III)-152, and americium(III)-241 was examined with respect to the time of phase equilibration, pH, sorbent dosage, and the presence of salts and complexing agents. Irradiation stability of the material was also studied. It was found that uptake of the radionuclides is almost complete. A procedure for the removal of technetium-99 has been also proposed. Experimental results obtained within the presented work confirm our expectations.