As a load-bearing tool, steel wire rope plays an important role in industrial production. Therefore, diagnosing the fracture and damage of steel wire ropes is of great significance for ensuring their safe operation. However, the detection and identification of wire rope breakage damage mainly focus on identifying external damage characteristics, while research on inspecting internal breakage damage is still relatively limited. To address the challenge, an intelligent detecting method is proposed in this paper for diagnosing internal wire breakage damage, and it introduces residual modules to enhance the network’s feature extraction ability. Firstly, time–frequency analysis techniques are used to convert the extracted one-dimensional magnetic flux leakage (MFL) signal into a two-dimensional time–frequency map. Secondly, the focus of this article is on constructing a residual network to identify the internal damage accurately with the features of the time–frequency map of the MFL signal being automatically extracted. Finally, the effectiveness of the proposed method in identifying broken wires is verified through comparative experiments on detecting broken wires in steel wire ropes. Three common recognition methods, the backpropagation (BP) neural network, the support vector machine (SVM), and the convolutional neural network (CNN), are used as comparisons. The experimental results show that the residual network recognition method can effectively identify internal and external wire breakage faults in steel wire ropes, which is of great significance for achieving quantitative detection of steel wire ropes.