Catalyzes the NAD-dependent decarboxylation of UDP-glucuronic acid to UDP-xylose (PubMed:22810237, PubMed:23656592, PubMed:25521717). Necessary for the biosynthesis of the core tetrasaccharide in glycosaminoglycan biosynthesis (PubMed:22810237, PubMed:23656592, PubMed:25521717).