Automatic Modulation Classification (AMC)-oriented Deep Neural Networks (ADNNs) have received much attention in recent years for their wide range of applications. However, they are vulnerable to attacks. Adversarial Examples (AEs) of modulation signals with added weak perturbations can easily fool ADNNs. The study of AEs on AMC, on one side, can enhance the security of wireless communication systems; on the other side, it can provide an effective defence against potential attacks. Nevertheless, most existing attack methods generate AEs with low transferability. In this paper, we propose a Multiscale Discriminative Attack Method (MDAM) for modulated signals. The method strives to alleviate such transferability issue by destroying discriminative features in multi-layer. Specifically, we utilize interpretable class activation maps to distinguish the discriminative regions, ignoring the noise and focusing on the interference of the discriminative features. Beyond that, we propose a multi-layer activation disruption loss to constrain activations in the middle layers. In so doing, the AEs do not erroneously retain deep features of the original signal. We conduct extensive experiments on RadioML datasets and the local area network (LAN) communication dataset we collected to evaluate the effectiveness of MDAM in both white-box and black-box attack scenarios. The results show that MDAM outperforms existing methods.