Catalyzes the deacetylation of N-acetylaspartic acid (NAA) to produce acetate and L-aspartate. NAA occurs in high concentration in brain and its hydrolysis NAA plays a significant part in the maintenance of intact white matter. In other tissues it act as a scavenger of NAA from body fluids (By similarity). H2O + N-acyl-L-aspartate = a carboxylate + L-aspartate Binds 1 zinc ion per subunit. Homodimer. Belongs to the AspA/AstE family. Aspartoacylase subfamily.