Styela clava is an edible sea squirt farmed in Korea that has gradually invaded other seas, negatively impacting the ecology and economy of coastal areas. Extracts from S. clava have shown wide bioactivities, and ascidians have the unique capability among animals of biosynthesizing cellulose. Thus, S. clava is a relevant candidate for valorization. Herein, we aimed at surveying and characterizing polysaccharides in both tunic and flesh of this ascidian. To this end, we enzymatically hydrolyzed both tissues, recovering crystalline cellulose from the tunic with high aspect ratios, based on results from microscopy, X-ray diffraction, and infrared spectroscopy analyses. Alkaline hydroalcoholic precipitation was applied to isolate the polysaccharide fraction that was characterized by gel permeation chromatography (with light scattering detection) and NMR. These techniques allowed the identification of glycogen in the flesh with an estimated Mw of 7 MDa. Tunic polysaccharides consisted of two fractions of different Mw. Application of Diffusion-Ordered NMR allowed spectroscopically separating the low-molecular-weight fraction to analyze the major component of an estimated Mw of 40–66 kDa. We identified six different sugar residues, although its complexity prevented the determination of the complete structure and connectivities of the residues. The two more abundant residues were N-acetylated and possibly components of the glycosaminoglycan-like (GAG-like) family, showing the remaining similarities to sulfated galactans. Therefore, Styela clava appears as a source of nanocrystalline cellulose and GAG-like polysaccharides.