The difference between physical activations (by sonications) and chemical activations (by ammonia) on sawdust biochar has been investigated in this study by comparing the removal of Cu(II) ions from an aqueous medium by adsorption on sawdust biochar (SD), sonicated sawdust biochar (SSD), and ammonia-modified sawdust biochar (SDA) with stirring at room temperature, pH value of 5.5–6.0, and 200 rpm. The biochar was prepared by the dehydrations of wood sawdust by reflux with sulfuric acid, and the biochar formed has been activated physically by sonications and chemically by ammonia solutions and then characterized by the Fourier transform infrared (FTIR); Brunauer, Emmett, and Teller (BET); scanning electron microscope (SEM); thermal gravimetric analysis (TGA); and energy-dispersive spectroscopy (EDX) analyses. The removal of Cu(II) ions involves 100 mL of sample volume and initial Cu(II) ion concentrations (conc) 50, 75, 100, 125, 150, 175, and 200 mg L−1 and the biochar doses of 100, 150, 200, 250, and 300 mg. The maximum removal percentage of Cu(II) ions was 95.56, 96.67, and 98.33% for SD, SSD, and SDA biochars, respectively, for 50 mg L−1 Cu(II) ion initial conc and 1.0 g L−1 adsorbent dose. The correlation coefficient (R2) was used to confirm the data obtained from the isotherm models. The Langmuir isotherm model was best fitted to the experimental data of SD, SSD, and SDA. The maximum adsorption capacities (Qm) of SD, SSD, and SDA are 91.74, 112.36, and 133.33 mg g−1, respectively. The degree of fitting using the non-linear isotherm models was in the sequence of Langmuir (LNR) (ideal fit) > Freundlich (FRH) > Temkin (SD and SSD) and FRH (ideal fit) > LNR > Temkin (SDA). LNR and FRH ideally described the biosorption of Cu(II) ions to SD and SSD and SDA owing to the low values of χ2 and R2 obtained using the non-linear isotherm models. The adsorption rate was well-ordered by the pseudo-second-order (PSO) rate models. Finally, chemically modified biochar with ammonia solutions (SDA) enhances the Cu(II) ions’ adsorption efficiency more than physical activations by sonications (SSD). Response surface methodology (RSM) optimization analysis was studied for the removal of Cu(II) ions using SD, SSD, and SDA biochars.