Chitosan is a well-studied biomaterial which has been widely used for environmental applications as an efficient natural polymer for the adsorption and removal of metal ions. Owing to its unique properties, chitosan shows good metal-binding behavior toward several different metal ions such as Cu2+, Zn2+, Cd2+, Ni2+, Co2+, and Ca2+. Chemical modifications with the introduction of functional groups have been carried out extensively and thereby producing various chitosan derivatives to increase the selectivity and adsorption capacity toward metal ions. The present work focuses on two such monofunctional derivatives, namely, carboxymethyl chitosan (CMC) and ethylenediaminetetraacetic acid chitosan (EDTA-CS) which have been recognized as excellent adsorbents for metal removal. The main objective of this study was to synthesize a new bifunctional chitosan derivative, namely, ethylenediaminetetraacetic acid–carboxymethyl chitosan (EDTA-CMC) by attaching both carboxymethyl and EDTA functional groups on the polymer backbone and thereby enhancing its metal-binding properties. The bifunctional derivative synthesis was conducted by combining the procedures of synthesis of CMC and EDTA-CS. Newly synthesized EDTA-CMC derivative was characterized by Fourier-transform infrared (FT-IR) spectroscopy, scanning electron microscope analysis, and thermogravimetric analysis. Adsorption properties of EDTA-CMC were investigated with Cu2+ ions which produced an adsorption capacity of 111.90 mg g−1 for 1000.0 mg/L and 12.20 mg g−1 for 10.00 mg/L Cu2+ solutions. The preliminary results revealed that EDTA-CMC is an effective adsorbent than CMC to remove Cu2+ in aqueous samples. The effects of pH, initial concentration, and mass of the adsorbent in the adsorption process were studied. Under the optimized parameters of an adsorbent dosage of 10.00 mg and pH 5.5, a comparable maximum adsorption capacity up to 112.44 mg g−1 was achieved with a 150.00 mg/L of Cu2+ solution. Furthermore, EDTA-CMC showed good adsorption performance even after five cycles of regeneration.