Biochar prepared from Triticum aestivum straw (SB) was used to investigate the sorption separation of Cd2+ and Co2+ ions in single and binary systems. The maximum adsorption capacity of SB was higher for Cd2+ ions and the process was strongly pH dependent. Adsorption data in the binary system Cd2+–Co2+ were well described by the extended Langmuir model and the values of affinity parameter b indicate a higher affinity of SB to Cd2+ in comparison with Co2+ ions. The mechanisms for the removal of Cd and Co by biochar were evidenced by the different instrumental analyses as well as by chemical speciation modeling. Elemental mapping of SB revealed spatial distributions of cobalt and cadmium on biochar surfaces. The role of functional groups in metal sorption was confirmed by FTIR. Results demonstrate that SB is a promising heavy metal-immobilizing agent for contaminated soils or water.