The competitive performance and selectivity for the separation of Co2+ and Ni2+ from Mn2+ solution by a triethylene-tetramine-modified cross-linked chitosan derivative were explored through the adsorption isotherm and kinetic models of single, binary, and ternary components in a static adsorptive experiment and in displacement experiments. In the single system, the adsorption capacities of Co2+, Ni2+, and Mn2+ onto the adsorbent followed the order of Ni2+ > Co2+ > Mn2+. As to binary and ternary systems, strong competitive and selective adsorption behaviors of Co2+ and/or Ni2+ over Mn2+ were observed. Separation factors suggested the extremely higher selectivity for Co2+ and Ni2+ against Mn2+. Displacement experiments showed that the initially adsorbed Mn2+ on the adsorbent could be displaced by subsequently adsorbed Co2+ and/or Ni2+ from the solution, but not the opposite. The results proved that the chitosan derivative was a potential and promising adsorbent for the selective removal of Co2+ and Ni2+ from manganiferous wastewater.