Plant waste materials are important sources of bioactive compounds with remarkable health-promoting benefits. In particular, industrial by-products such as mango peels are sustainable sources of bioactive substances, with antioxidant, enzymatic, and antimicrobial activity. Appropriate processing is essential to obtain highly bioactive compounds for further use in generating value-added products for the food industry. The objective of the study was to investigate and compare the biological activity of compounds from fresh and dried mango peels obtained by different conventional methods and unconventional extraction methods using supercritical fluids (SFE). The highest total phenolic content (25.0 mg GAE/g DW) and the total content of eight phenolic compounds (829.92 µg/g DW) determined by LC-MS/MS were detected in dried mango peel extract obtained by the Soxhlet process (SE). SFE gave the highest content of proanthocyanidins (0.4 mg PAC/g DW). The ethanolic ultrasonic process (UAE) provided the highest antioxidant activity of the product (82.4%) using DPPH radical scavenging activity and total protein content (2.95 mg protein/g DW). Overall, the dried mango peels were richer in bioactive compounds (caffeic acid, chlorogenic acid, gallic acid, catechin, and hesperidin/neohesperidin), indicating successful preservation during air drying. Furthermore, outstanding polyphenol oxidase, superoxide dismutase (SOD), and lipase activities were detected in mango peel extracts. This is the first study in which remarkable antibacterial activities against the growth of Gram-negative bacteria (Escherichia coli and Pseudomonas aeruginosa) and Gram-positive bacteria (Bacillus cereus and Staphylococcus aureus) were evaluated by determining the microbial growth inhibition rate after 12 and 24 h incubation periods for mango peel extracts obtained by different methods. Ethanolic SE and UAE extracts from dried mango peels resulted in the lowest minimum inhibitory concentrations (MIC90) for all bacterial species tested. Mango peels are remarkable waste products that could contribute to the sustainable development of exceptional products with high-added value for various applications, especially as dietary supplements.