Neutrophil extracellular traps (NETs) are produced by neutrophils as an innate immune defense mechanism to trap and kill microbial pathogens. NETs are comprised of ejected chromatin that forms a lattice structure enmeshed with numerous antimicrobial proteins. In addition to forming the structural backbone of NETs, extracellular DNA (eDNA) has membrane-disrupting antimicrobial activity that contributes to NET killing. Many pathogens produce secreted extracellular DNases to evade the antimicrobial activity of NETs. Pseudomonas aeruginosa encodes an operon of two secreted enzymes, a predicted alkaline phosphatase and a DNase. The DNase (eddB) degrades eDNA to use as a nutrient source. Here we report that both eDNA and NETs are potent inducers of this DNase-phosphatase operon. Furthermore, the secreted DNase contributes to degrading NET DNA and defends P. aeruginosa against NET-mediated killing. We demonstrate that EddA has both alkaline phosphatase and phosphodiesterase (PDase) activities and also protects against the antimicrobial activity of NETs. Although the phosphatase does not cause DNA degradation similar to that of the DNase, its protective function is likely a result of removing the cation-chelating phosphates from the eDNA phosphodiester backbone. Therefore, both the DNase and PDase contribute to defense against NET killing of P. aeruginosa, highlighting the role of DNA-manipulating enzymes in targeting the eDNA in neutrophil extracellular traps.