The processing of Mexican limes generates great amounts of peel as a by-product. Lime peel is mainly rich in the flavonoid hesperidin, whose bioactivity is oriented mainly to cardiovascular diseases and cancer. The purpose of this work was to develop a green process for the extraction and purification of hesperidin from Mexican lime peel. The extraction of hesperidin was investigated on a laboratory scale by varying the solvent composition and the solid-to-solvent ratio, and then scaling this process (volume: 20 L). Next, a purification process using adsorption resins was assessed: first through static tests to determine the adsorption efficiency with two resins (FPX66, EXA118), and then on a packed column with 80 mL of resin at 25 °C. Lab-scale extraction showed that the best conditions were a solid-to-solvent ratio of 0.33 g/mL and 60% ethanol. After using these conditions at pilot scale and concentrating the solution, the hesperidin content of the extract was 0.303 mg/mL. Through static tests, higher adsorption efficiencies were achieved with the EXA-118 resin and diluted extract (4:6 ratio with 10% dimethylsulfoxide, (DMSO)). Finally, the purification process on a packed column from the diluted extract (hesperidin concentration of 0.109 mg/mL) had a mean recovery efficiency of almost 90%.