Incorporating recycled polyethylene terephthalate (PET) into asphalt mixtures offers a sustainable approach to enhance pavement performance while reducing plastic waste. However, the mesoscale mechanisms governing the influence of PET on stiffness, deformation resistance, and fracture behavior remain unclear. In this study, a three-dimensional Discrete Element Method (DEM) framework was developed to investigate the constitutive response of PET-modified asphalt concrete through the explicit representation of aggregates, asphalt mortar, PET inclusions, and air voids. Two bonding schemes, the Contact Bond Model (CBM) and Parallel Bond Model (PBM), were implemented and compared in terms of stiffness, tensile strength, damage evolution, and crack propagation. The experimental dynamic modulus (|E*|), indirect tensile strength (ITS), resilient modulus (Mr), rutting, and moisture susceptibility tests were conducted for mixtures containing 0–10% PET by volume. The DEM microparameters were calibrated using |E*| and ITS data, whereas Mr, rut depth, and tensile strength ratio (TSR) were used for independent validation. The results show that PET incorporation increases the mixture stiffness, with the dynamic modulus rising from 3500 to 5159 MPa and improves the resilient response under repeated loading. ITS increased from 0.44 MPa for the control mixture to a peak value of 1.15 MPa at 6% PET before decreasing to 0.89 MPa at 10% PET due to interfacial weakening. The rut depth decreased consistently with increasing PET content, indicating enhanced resistance to permanent deformation, whereas the TSR values confirmed acceptable moisture durability. Mesoscale analyses revealed that PET modified the force-chain distribution and promoted interface-controlled damage at the PET–mortar contacts. Compared with CBM, PBM more accurately reproduces progressive stiffness degradation and distributed cracking. An optimum PET content of approximately 6% was identified, providing the best balance between stiffness enhancement, tensile resistance and durability. These findings provide mechanistic insights into PET-modified asphalt mixtures and support the development of performance-based sustainable pavement materials.