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Network pruning has been the driving force for the acceleration of neural networks and the alleviation of model storage/transmission burden. With the advent of AutoML and neural architecture search (NAS), pruning has become topical with automatic mechanism and searching based architecture optimization. Yet, current automatic designs rely on either reinforcement learning or evolutionary algorithm. Due to the non-differentiability of those algorithms, the pruning algorithm needs a long searching stage before reaching the convergence. To circumvent this problem, this paper introduces a differentiable pruning method via hypernetworks for automatic network pruning. The specifically designed hypernetworks take latent vectors as input and generate the weight parameters of the backbone network. The latent vectors control the output channels of the convolutional layers in the backbone network and act as a handle for the pruning of the layers. By enforcing $\ell_1$ sparsity regularization to the latent vectors and utilizing proximal gradient solver, sparse latent vectors can be obtained. Passing the sparsified latent vectors through the hypernetworks, the corresponding slices of the generated weight parameters can be removed, achieving the effect of network pruning. The latent vectors of all the layers are pruned together, resulting in an automatic layer configuration. Extensive experiments are conducted on various networks for image classification, single image super-resolution, and denoising. And the experimental results validate the proposed method.