We studied photoluminescence (PL) properties and nonlinear absorption characteristics of heavily Cu-doped CdSe colloidal quantum dots (QDs) under nanosecond laser pulse excitation. A strong dependence of basic exciton transition behavior and Cu dopant-associated PL on the concentration of copper ions and pump intensities was revealed for the first time. The saturation of the copper-associated PL signal was found to happen much faster than the saturation of nonlinear absorption. The induced absorption and saturation of high energy transitions due to the exciton-exciton interaction were investigated in Cu-doped CdSe QDs. The obtained results could be useful for the development of optoelectronic devices operating at room temperature on the basis of Cu-doped colloidal QDs.