Pseudomonas aeruginosa is a leading cause of nosocomial infections worldwide and notorious for its broad-spectrum resistance to antibiotics. A key mechanism that provides extensive resistance to β-lactam antibiotics is the inducible expression of AmpC β-lactamase. Recently, a number of clinical isolates expressing mutated forms of AmpC have been found to be clinically resistant to the antipseudomonal β-lactam/β-lactamase inhibitor (BLI) combinations ceftolozane/tazobactam and ceftazidime/avibactam. Here, we compare the enzymatic activity of wild-type (WT) AmpC from PAO1 to four of these reported AmpC mutants, E247K, G183D, T96I, and ΔG229–E247, to gain detailed insights into how these mutations circumvent these clinically vital antibiotic/inhibitor combinations. We found that these mutations exert a twofold effect on the catalytic cycle of AmpC. First, they reduce the stability of the enzyme, thereby increasing its flexibility. This appears to increase the rate of deacylation of the enzyme-bound β-lactam, resulting in greater catalytic efficiencies towards ceftolozane and ceftazidime. Second, these mutations reduce the affinity of avibactam for AmpC by increasing the apparent activation barrier of the enzyme acylation step. This does not influence the catalytic turnover of ceftolozane and ceftazidime significantly, as deacylation is the rate-limiting step for the breakdown of these antibiotic substrates. It is remarkable that these mutations enhance the catalytic efficiency of AmpC towards ceftolozane and ceftazidime while simultaneously reducing susceptibility to inhibition by avibactam. Knowledge gained from the molecular analysis of these and other AmpC resistance mutants we believe will help aid the design of β-lactams and BLIs with reduced susceptibility to mutational resistance.