The extraction of clary sage (Salvia sclarea L.) using supercritical carbon dioxide (SC-CO2) was systematically studied by using thin layer chromatography-direct bioautography (TLC-DB) and response surface methodology (RSM). The three parameters temperature, pressure, and cosolvent ratio were optimized for the maximum antibacterial activity of clary sage extracts against Pseudomonas aeruginosa (P. aeruginosa) and methicillin-resistant Staphylococcus aureus (MRSA). The highest inhibition zone was 7.51 mm for P. aeruginosa and 7.57 mm for MRSA. According to RSM analysis, the predicted optimum extraction parameters are 18.6 MPa pressure, 40 °C temperature, and 2% ethanol (EtOH) ratio. The combination of this analytical and statistical method allows saving time, money, and instrument runtime in the optimization of essential oil composition, which is tailored to a specific task and could be useful on any kind of herbs in a wide range of use from perfume manufacturing to the food industry.