Arthrospira maxima has been identified as a sustainable source of rich proteins with diverse functionalities and bioactivities. After extracting C-phycocyanin (C-PC) and lipids in a biorefinery process, the spent biomass still contains a large proportion of proteins with potential for biopeptide production. In this study, the residue was digested using Papain, Alcalase, Trypsin, Protamex 1.6, and Alcalase 2.4 L at different time intervals. The resulting hydrolyzed product with the highest antioxidative activity, evaluated through their scavenging capability of hydroxyl radicals, superoxide anion, 2,2-diphenyl-1-picrylhydrazyl (DPPH), and 2,2'-azino-bis (3-ethylbenzothiazoline-6-sulfonic acid (ABTS), was selected for further fractionation and purification to isolate and identify biopeptides. Alcalase 2.4 L was found to produce the highest antioxidative hydrolysate product after four-hour hydrolysis. Fractionating this bioactive product using ultrafiltration obtained two fractions with different molecular weights (MW) and antioxidative activity. The low-molecular-weight fraction (LMWF) with MW <3 kDa had higher DPPH scavenging activity with the IC 50 value of 2.97 ± 0.33 compared to 3.76 ± 0.15 mg/mL of the high-molecular-weight fraction (HMWF) with MW >3 kDa. Two stronger antioxidative fractions (F-A and F-B) with the respective significant lower IC 50 values of 0.83 ± 0.22 and 1.52 ± 0.29 mg/mL were isolated from the LMWF using gel filtration with a Sephadex G-25 column. Based on LC-MS/MS analysis of the F-A, 230 peptides derived from 108 A. maxima proteins were determined. Notably, different antioxidative peptides possessing various bioactivities, including antioxidation, were detected with high predicted scores together with in silico analyses on their stability and toxicity. This study established knowledge and technology to further value-add to the spent A. maxima biomass by optimizing hydrolysis and fraction processes to produce antioxidative peptides with Alcalase 2.4 L after two products already produced in a biorefinery. These bioactive peptides have potential applications in food and nutraceutical products.