Hydrogels have demonstrated significant potential in wound dressings, owing to their adjustable water content, excellent biocompatibility, and other advantages. An ideal wound dressing requires absorbing exudate while maintaining mechanical properties to prevent secondary damage to the wound under external pressure. In this study, Polyacrylic Acid (PAA)/Chitosan (CS) double network hydrogels were prepared via radical polymerization, and the swelling ratio, compressive modulus, and other parameters were experimentally measured. A hyperelastic finite element model of the hydrogel was then established, and its rationality was validated by experiments. Based on the model, the impacts of CS content and dynamic water content on the compressive properties of PAA/CS hydrogels were analyzed. Tetracycline hydrochloride was loaded into PAA/CS hydrogels, the drug release performance and adhesion experiments were carried out. The results indicated that, compared with the hydrogels with 2.5% and 5% CS content, the hydrogel with 1% CS content had the highest swelling ratio, which was 1774%. Meanwhile, its equilibrium water content could attain 94.6%. When the water content varied within the range from 45% to 75%, the compressive strength of the hydrogel with 5% CS content ranged from 0.33 MPa to 1.22 MPa, similar to that of skin tissue. Additionally, the prepared drug-loaded PAA/CS hydrogels exhibited a drug release pattern approximately following the Korsmeyer-Peppas model within 7 days. They also exhibited remarkable adhesion to porcine skin and different substrate surfaces. This study provides a basis for the clinical application of PAA/CS double network hydrogels as wound dressings in the repair of infected wounds.