Colombian mango production, which exceeded 261,000 t in 2020, generates about 40% of the whole fruit as solid waste, of which more than 50% are seed kernels (over 52,000 t solid by-product); though none is currently used for commercial purposes. This study reports the results of the supercritical carbon dioxide (scCO2) extraction of an oil rich in essential fatty acids (EFAs) from revalorized mango seed kernels and the optimization of the process by the Response Surface Methodology (RSM). In pilot-scale scCO2 experiments, pressure (23 MPa–37 MPa) and temperature (52 °C–73 °C) were varied, using 4.5 kg of CO2. The highest experimental oil extraction yield was 83 g/kg (37 MPa and 63 °C); while RSM predicted that 84 g/kg would be extracted at 35 MPa and 65 °C. Moreover, by fine-tuning pressure and temperature it was possible to obtain an EFA-rich lipid fraction in linoleic (37 g/kg) and α-linolenic (4 g/kg) acids, along with a high oleic acid content (155 g/kg), by using a relatively low extraction pressure (23 MPa), which makes the process a promising approach for the extraction of oil from mango waste on an industrial scale, based on a circular economy model.