Organophosphate hydrolases are proficient catalysts of the breakdown of neurotoxic organophosphates and have great potential as both biotherapeutics for treating acute organophosphate toxicity and as bioremediation agents. However, proficient organophosphatases such as serum paraoxonase 1 (PON1) and the organophosphate-hydrolyzing lactonase SsoPox are unable to hydrolyze bulkyorganophosphates with challenging leaving groups such as diisopropyl fluorophosphate (DFP) or venomous agent X, creating a major challenge for enzyme design. Curiously, despite their mutually exclusive substrate specificities, PON1 and diisopropyl fluorophosphatase (DFPase) have essentially identical active sites and tertiary structures. In the present work, we use empirical valence bond simulations to probe the catalytic mechanism of DFPase as well as temperature, pH, and mutational effects, demonstrating that DFPase and PON1 also likely utilize identical catalytic mechanisms to hydrolyze their respective substrates. However, detailed examination of both static structures and dynamical simulations demonstrates subtle but significant differences in the electrostatic properties and solvent penetration of the two active sites and, most critically, the role of residues that make no direct contact with either substrate in acting as "specificity switches" between the two enzymes. Specifically, we demonstrate that key residues that are structurally and functionally critical for the paraoxonase activity of PON1 prevent it from being able to hydrolyze DFP with its fluoride leaving group. These insights expand our understanding of the drivers of the evolution of divergent substrate specificity in enzymes with identical active sites and guide the future design of organophosphate hydrolases that hydrolyze compounds with challenging leaving groups.