To elucidate the working mechanism of the "broad substrate specificity" by the Pseudomonas aeruginosa aryl sulfatase (PAS) enzyme, we present here a full quantum chemical study performed at the density functional level. This enzyme is able to catalyze the hydrolysis of the original p-nitrophenyl-sulfate (PNPS) substrate and the promiscuous p-nitrophenyl-phosphate (PNPP) one with comparable reaction kinetics. Based on the obtained results, a multistep mechanism including activation of the nucleophile, the nucleophilic attack, and the cleavage of the S-O (P-O) bond is proposed. Regarding the phosphate monoester, the results indicate that only some steps of the promiscuous reaction are identical to those in the native process. Differences concern mainly the last step in which the His115 residue acts as a general base to accept the proton by the O atom of the FGly51 in the PNPS, whereas in PNPP, the Asp317 protonated residue works as a general acid to deliver a proton by a water molecule to the oxygen atom of the C-O bond. The shapes of the relative potential-energy surface (PES) are similar in the two examined cases but the rate-determining step is different (nucleophile attack vs. nucleophile activation). The influence of the dispersion contributions on the investigated reactions was also taken into account.