To address the deficiencies in existing methods for bridge damage identification using vehicle response, a new approach integrating vehicle-bridge coupled vibration and deep learning theory is proposed. Taking the self-anchored suspension bridge of Zhengzhou Taohuayu as an example, finite element analysis models of the bridge and vehicles are established. A vehicle-bridge coupled vibration analysis is conducted on the large-span self-anchored suspension bridge to obtain vehicle acceleration responses. Using these acceleration responses as input parameters, two deep learning models—one-dimensional convolutional neural network (1D-CNN) and two-dimensional convolutional neural network (2D-CNN)—are constructed and their identification effectiveness is compared. The influence of factors such as signal noise and low damage conditions on the bridge structure damage identification effectiveness is explored. Results indicate that the 2D-CNN surpasses the 1D-CNN in terms of accuracy and training efficiency for bridge damage identification; the 1D-CNN achieves end-to-end intelligent damage identification, while the 2D-CNN demonstrates superior performance in accuracy and robustness against external interference. The research results provide a reference for further optimization of bridge structure damage identification methods.