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, preserving its antioxidant activity. The assessment with reference to the extraction of phenolic compounds, as well as their capacity to scavenge ABTS and the antioxidant capacity, determined by the modified DPPH method were investigated based on distinct combinations of time, temperature, velocity of rotation and solvents concentration. It was investigated that the optimum condition for the highest antioxidant yield was obtained using water (60.84%), acetone (30.31%) and ethanol (8.85%) at 30 ºC during 20 min at 50 rpm. We have found that the maximum yield of total phenolics was 355.63 ± 9.77 (mg GAE/100 g), showing an EC50 of 3962.24 ± 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 preserving its antioxidant activity. This method does not require expensive reagents or high quantities of organic solvents.