This study explored the use of mandarin peels as an important source of health-promoting compounds by utilizing green methods (i.e., pulsed electric field and ultrasound-assisted extraction), along with conventional stirring. The impact of several extraction parameters, such as extraction duration, temperature, and solvent composition, on the recovery of bioactive compounds was evaluated through a response surface methodology. To identify the most effective conditions for all assays, a partial least-squares analysis was implemented. It was revealed that a combination of the above techniques was optimal at 80 °C for 30 min, with 75% v/v of ethanol in water as the extraction solvent. The concentration of bioactive compounds in the optimum extract had a total polyphenol content of 18.69 mg of gallic acid equivalents (GAE) per gram of dry weight (dw), and an ascorbic acid concentration of 18.25 mg/g dw. However, correlation analyses revealed a rather negative relationship between these bioactive compounds. The chromatographic analysis of optimum extracts supported this result by quantifying 20.53 mg/g dw of total individual polyphenols, with hesperidin being the dominant compound (13.98 mg/g dw). The antioxidant assays, including ferric-reducing antioxidant power and DPPH• inhibition activity, were measured at 123.21 and 65.12 μmol of ascorbic acid equivalents (AAE) per gram of dw, respectively. This research enhances the valorization of mandarin peels as a renewable source of bioactive compounds, providing the opportunity to generate high-added-value products from food waste in the food and pharmaceutical sectors.