Spent coffee grounds (SCGs) have great potential as a useful, value-added biological material. In this context, activated carbon (AC) was prepared from SCGs by an activation process using H3PO4 at 600 °C in the air and used as an adsorbent for the azo dye AO7, a model molecule for dye colorants found in textile industry effluents. X-ray diffraction, SEM and BET revealed that the AC was predominantly amorphous, consisting of a powder of 20–100 µm particles with mesopores averaging 5.5 nm in pore size. Adsorption kinetics followed a pseudo-second-order law, while the Langmuir model best fitted the experimental isotherm data (maximum capacity of 119.5 mg AO7 per AC g). The thermodynamic parameters revealed that adsorption was endothermic and spontaneous. All the characterizations indicated that adsorption occurred by physisorption via mainly π–π interactions. The best experimental removal efficiency optimized by means of a Box–Behnken design and response surface methodology was 98% for an initial AO7 concentration of 20 mg·L−1 at pH 7.5 with a dose of 0.285 g·L−1 of AC and a contact time of 40 min. These results clearly show that activated carbon prepared from SCGs can be a useful material for efficiently removing organic matter from aqueous solutions.