This study aimed to extract tiger nut polysaccharides (TNPs) by the cellulase method which were graded using the DEAE-cellulose ion exchange method to obtain neutral (TNP-N) and acidic (TNP-A) polysaccharide classes. Analysis of the physical structures and monosaccharide compositions of TNP-A (3.458 KDa) and TNP-N (10.640 KDa) revealed lamellar and dense flocculent structures, with both primarily containing the monosaccharides glucose, galactose, and arabinose (Glc, Gal, and Ara). Single-factor and orthogonal tests were used to select three hydrocolloids, and the optimal ratio of the composite hydrocolloids was determined. Peanut protein drinks with a centrifugal sedimentation rate of 9.71% and a stability factor of 69.28% were obtained by adding 2.78% polysaccharide extract, 0.1% monoglyceride, and peanut pulp at a ratio of 1:15.5 g/mL. Polysaccharide protein drinks are more stable than commercially available protein drinks, with nutritional parameters either comparable to or better than those of the non-polysaccharide protein drinks.