A fast method for preparing aqueous graphene oxide (GO) dispersions by electrochemical oxidation of a graphite anode without preliminary intercalation with oxidizing agents is proposed. Ultrasonic probing was used in the modulation mode of ultrasonic waves (work/rest) for more efficient graphite oxidation–exfoliation. It is shown that the 4/2 s mode of ultrasonic modulation is the most effective due to the probe material’s low corrosion while maintaining the optimum synthesis temperature not exceeding 30–35 °C and achieving the best characteristics of the resulting product. Three cases of anodic oxidation of graphite to obtain graphene oxide were considered: (1) a combined cathode–anode compartment, (2) a split cathode–anode salt-bridged compartment, and (3) separated anode compartment with a 3.5 kDa dialysis membrane. It was determined that the approach to synthesis with a divided cathode–anode compartment makes it possible to obtain GO sheets with fewer defects compared to chemical methods or methods with a combined cathode–anode compartment and makes it possible to control the oxidation degree of the material (C:O ratio) by varying the current density. The prepared samples showed good stability for more than six months. The spectral and morphological characteristics were studied. Using chemiluminometry in the luminol/Co(II)/H2O2 system, the antioxidant properties concerning three key reactive oxygen species (H2O2, superoxide anion radical, and hydroxyl radical) were demonstrated. It was also shown that the prepared GO dispersions do not induce lipid and phospholipid peroxidation.