Existing studies have extensively investigated the global dynamic response of bridge piers under vehicle impact; however, most of them focus on frontal collisions, and the pier response under eccentric collisions remains insufficiently clarified. This study conducts a numerical investigation on the dynamic response of a circular bridge pier subjected to eccentric vehicle impact. A validated finite element model for vehicle-circular pier collision is established. Comparative analyses are performed between different eccentricity levels and the frontal-impact case in terms of failure-mode evolution, impact-force time histories, and key-section displacement responses. In addition, the effects of impact velocity and vehicle mass on the dynamic response under eccentric collision are examined. The results indicate that when the eccentricity is less than 60%, the damage in the impacted region and the bending cracks on the rear face are generally less severe than those under a central frontal collision. As the eccentricity increases such that the engine no longer directly participates in contact, the collision mechanism shifts, and the overall damage level becomes higher than that of the central frontal collision. The velocity effect is non-linear; when the speed increases to 120 km/h, damage is markedly aggravated, accompanied by a significant increase in peak structural displacement. Mass parameters exhibit stage-dependent dominance: the engine mass mainly governs the flexural-shear response during the engine-contact phase, whereas increasing cargo mass substantially amplifies the impact effect in the cargo-contact phase, promoting the pier damage from localized cracking to more extensive flexure-dominated failure.