Arthrospira is one of the most studied cyanobacteria and has been reported with practical applications. Among the substances derived from Arthrospira, polysaccharides have received relatively less attention than phycocyanins, though they have more abundant structural variations and specific properties. Herein, a new Arthrospira-derived sulfated polysaccharide was explored for its potential bioactive functions. The ability of this sulfated polysaccharide to promote the behavior of neural stem cells (NSCs) in three-dimensional hydrogel was examined for the first time. NSCs encapsulated in the sulfated polysaccharide-containing hydrogel showed better proliferation than the control hydrogel as well as a unique cell clustering behavior, i.e., formation of multicellular spherical clusters (40–60 μm). The sulfated polysaccharide, in an appropriate range of concentration (5 mg/mL), also maintained the stemness of NSCs in hydrogel and facilitated their differentiation. In addition, the potentials of the new sulfated polysaccharide as a coating material and as a component for drug carrier were verified. The sulfated polysaccharide-modified substrate exhibited superhydrophilicity (contact angle ~9°) and promoted cell adhesion to the substrate. Composite nanoparticles composed of the sulfated polysaccharide and other differently charged polysaccharides were produced with an average diameter of ~240 nm and estimated drug loading of ~18%. The new Arthrospira-derived sulfated polysaccharide is a promising candidate for cell culture, surface-modification, and drug-delivery applications in the biomedical field.