Several chemical analytical methods were applied to characterize the chemical structure of polysaccharides extracted from discarded apples and pomegranate peels using hydrodynamic cavitation methods in a circular economy perspective. In particular, the purity of the polysaccharides and the degrees of acetylation and methylation were evaluated by proton Nuclear Magnetic Resonance (1H-NMR) analysis; simple sugars and galacturonic acid were analyzed simultaneously by High-Performance Anion Exchange Chromatography—Pulsed Amperometric Detector (HPAEC-PAD); the molecular weight of the extracted polysaccharides was determined by High-Performance Size Exclusion Chromatography-Refractive Index Detector (HPSEC-RID). The results showed a negligible presence of co-precipitated proteins/tannins, easily removed by dialysis, as well as other co-precipitated molecules such as monosaccharides and organic acids. Polysaccharides from apples consisted mainly of pectic material with a prevalence of homogalacturonans. Polysaccharides from pomegranate peels showed greater compositional variability with significant amounts of arabinose and galactose, a lower content of pectin, and the presence of rhamnogalacturonans I. Both polysaccharides were highly methylated and differed in the degree of acetylation, which could lead to different properties. Polysaccharides from apples presented two main molecular weights (>805 kDa and 348–805 kDa, respectively), while those from pomegranate peel showed a major fraction at 348 kDa and minor fractions < 23 kDa. In conclusion, the research tools proposed by this study have allowed defining the macrostructure of polysaccharides in a quick and efficient way to valorize these food by-products.