Catalyzes the conversion of UDP-D-glucuronate to a mixture of UDP-D-apiose and UDP-D-xylose. D-Apiose (3-C-hydroxymethyl-d-erythrose) is the only plant cell wall monosaccharide with a branched carbon skeleton and is found in rhamnogalacturonan II (RG-II), apiogalacturonan, and several apioglycosides (By similarity). Homodimer. Belongs to the NAD(P)-dependent epimerase/dehydratase family.