Biofilms are communities of bacteria embedded in a polymeric matrix which are found in infections and in environments outside the body. Breaking down the matrix renders biofilms more susceptible to physical disruption and to treatments such as antibiotics. Different species of bacteria, and different strains within the same species, produce different types of matrix polymers. This suggests that targeting specific polymers for disruption may be more effective than nonspecific approaches to disrupting biofilm matrixes. In this study, we treated Pseudomonas aeruginosa biofilms with enzymes that are specific to different matrix polymers. We measured the resulting alteration in biofilm mechanics using bulk rheology and changes in structure using electron microscopy. We find that, for biofilms grown in vitro, the effect of enzymatic treatment is greatest when the enzyme is specific to a dominant matrix polymer. Specifically matched enzymatic treatment tends to reduce yield strain and yield stress and increase the rate of biofilm drying, due to increased diffusivity as a result of network compromise. Electron micrographs qualitatively suggest that well-matched enzymatic treatments reduce long-range structure and shorten connecting network fibers. Previous work has shown that generic glycoside hydrolases can cause dispersal of bacteria from in vivo and ex vivo biofilms into a free-swimming state, and thereby make antibiotic treatment more effective. For biofilms grown in wounded mice, we find that well-matched treatments that result in the greatest mechanical compromise in vitro induce the least dispersal ex vivo. Moreover, we find that generic glycoside hydrolases have no measurable effect on the mechanics of biofilms grown in vitro, while previous work has shown them to be highly effective at inducing dispersal in vivo and ex vivo. This highlights the possibility that effective approaches to eradicating biofilms may depend strongly on the growth environment.