Catalysis of the reaction: beta-D-glucosaminyl-(1->4)-N-acetyl-D-glucosamine + H2O = D-glucosamine + N-acetyl-D-glucosamine.
2-acetamido-4-O-(2-amino-2-deoxy-beta-D-glucopyranosyl)-2-deoxy-D-glucose exo-beta-D-glucosaminidase activity