As deep neural networks (DNNs) are growing larger, their requirements for computational resources become huge, which makes outsourcing training more popular. Training in a third-party platform, however, may introduce potential risks that a malicious trainer will return backdoored DNNs, which behave normally on clean samples but output targeted misclassifications whenever a trigger appears at the test time. Without any knowledge of the trigger, it is difficult to distinguish or recover benign DNNs from backdoored ones. In this paper, we first identify an unexpected sensitivity of backdoored DNNs, that is, they are much easier to collapse and tend to predict the target label on clean samples when their neurons are adversarially perturbed. Based on these observations, we propose a novel model repairing method, termed Adversarial Neuron Pruning (ANP), which prunes some sensitive neurons to purify the injected backdoor. Experiments show, even with only an extremely small amount of clean data (e.g., 1%), ANP effectively removes the injected backdoor without causing obvious performance degradation.