Yak whey protein concentrates (YWPCs) have good functional properties, but there is still a gap in the study of their peptides. In this study, peptides were obtained by enzymatic hydrolysis, and the bioactivity of each ultrafiltration fraction was evaluated using an optimal process. YWPCs were isolated and purified from yak milk as the raw material. Alkaline protease, trypsin, and papain were used to hydrolyze YWPCs. The protease with the highest degree of hydrolysis (DH) and peptide concentration was selected as the most suitable enzyme. The effects of pH, temperature, time, and the enzyme-to-substrate ratio (E/S) on the DH and peptide concentration were investigated, and response surface methodology was utilized to optimize the hydrolysis process. The hydrolysate was separated using ultrafiltration membranes with molecular weight cut-offs of 10 kDa, 5 kDa, 3 kDa, and 1 kDa. The bioactivity of each ultrafiltration component was analyzed, including the inhibition rates of α-amylase and xanthine oxidase (XOD) activities and the scavenging rates of 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) cation radicals. The results indicated that alkaline protease was the best enzyme for hydrolyzing YWPCs. The peptide concentration in the YWPC hydrolysate was the highest (17.21 mg/mL) at a pH of 8 and a concentration of 7500 U/g, after 2.5 h at 62 °C. The enzymatic hydrolysate was ultrafiltered to yield four peptide fractions, of which the <1 kDa peptides exhibited the highest α-amylase inhibitory activity (22.06%), XOD inhibitory activity (17.15%), and ABTS cationic free radical scavenging rate (69.55%). This demonstrates the potential of YWPC hydrolyzed peptides for hypoglycemic, uric acid-lowering, and antioxidant applications, providing a theoretical basis for the high-value utilization of YWPCs.