Antimicrobial resistance reduces the efficacy of antibiotics. Infections caused by multidrug-resistant (MDR), Gram-negative bacterial strains, such as Klebsiella pneumoniae (MDRKp) and Pseudomonas aeruginosa (MDRPa), are a serious threat to global health. However, cationic antimicrobial peptides (CAMPs) are promising as an alternative therapeutic strategy against MDR strains. In this study, the inhibitory activity of a cationic peptide, derived from cecropin D-like (ΔM2), against MDRKp and MDRPa clinical isolates, and its interaction with membrane models and bacterial genomic DNA were evaluated. In vitro antibacterial activity was determined using the broth microdilution test, whereas interactions with lipids and DNA were studied by differential scanning calorimetry and electronic absorption, respectively. A strong bactericidal effect of ΔM2 against MDR strains, with minimal inhibitory concentration (MIC) and minimal bactericidal concentrations (MBC) between 4 and 16 μg/mL, was observed. The peptide had a pronounced effect on the thermotropic behavior of the 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC)/1,2-dimyristoyl-sn-glycero-3-phosphorylglycerol (DMPG) membrane models that mimic bacterial membranes. Finally, the interaction between the peptide and genomic DNA (gDNA) showed a hyperchromic effect, which indicates that ΔM2 can denature bacterial DNA strands via the grooves.