A new approach to extract pectin from clementine peel using citric acid/sodium citrate solutions (CSS) at different pHs as green extracting agents was proposed. In this study, the effects of extraction temperature (65–85 °C), CSS pH (2–8), and extraction time (1–3 h) on the extraction yield, uronic acid content, and degree of methyl esterification (DE) of the clementine peel pectin (CMP) were systematically evaluated by response surface methodology (RSM). Compared with traditional methods, the CMP extracted by this new approach was of higher pectin yield (19.90–34.94%) and uronic acid content (44.96–65.11%), as well as a wide DE value (11.05–84.71%). These functional properties of CMP were mainly determined by the CSS pH and extraction temperature. In comparison with commercial citrus pectin (CP), the extracted CMPs showed lower protein contents and larger molecular weights. The analysis of monosaccharide compositions showed that the high- and low-methyl-esterified CMPs were dominated by homogalacturonans and rhamnogalacturonan-I, respectively. The structural differences between high- and low-methyl-esterified CMPs were identified by their FTIR spectra. Especially, an excellent gel-forming capacity was found in low-methyl-esterified CMP solutions since their rheological behaviors were highly sensitive to low pH and the presence of Ca2+.