In this study, we have determined, using RSM (mixture design and Doehlert matrix), the optimum values of the independent variables to achieve the maximum response for the extraction of total phenolic compounds from Spondias mombin L bagasse agroindustrial residues in order to preserve their antioxidant activity. The extraction of phenolic compounds, as well as their antioxidant capacity and the capacity to scavenge ABTS, was determined by the modified DPPH method at different periods of time, temperature, velocity of rotation and solvents concentration. We observed that the optimum condition for the highest antioxidant yield was obtained using water (60.84%), acetone (30.31%), and ethanol (8.85%) at 30°C during 20 min at 50 rpm. We have also found that the maximum yield of total phenolics was 355.63 ± 9.77 (mg GAE/100 g), showing an EC50 of 3,962.24 ± 41.20 (g fruit/g of DPPH) and 8.36 ± 0.30 (μM trolox/g fruit), which were measured using DPPH and ABTS assays. These results suggest that RSM was successfully applied for optimizing the extraction of phenolics compounds thus preserving their antioxidant activity.