Neural network compression has gained increasing attention in recent years, particularly in computer vision applications, where the need for model reduction is crucial for overcoming deployment constraints. Pruning is a widely used technique that prompts sparsity in model structures, e.g. weights, neurons, and layers, reducing size and inference costs. Structured pruning is especially important as it allows for the removal of entire structures, which further accelerates inference time and reduces memory overhead. However, it can be computationally expensive, requiring iterative retraining and optimization. To overcome this problem, recent methods considered one-shot setting, which applies pruning directly at post-training. Unfortunately, they often lead to a considerable drop in performance. In this paper, we focus on this issue by proposing a novel one-shot pruning framework that relies on explainable deep learning. First, we introduce a causal-aware pruning approach that leverages cause-effect relations between model predictions and structures in a progressive pruning process. It allows us to efficiently reduce the size of the network, ensuring that the removed structures do not deter the performance of the model. Then, through experiments conducted on convolution neural network and vision transformer baselines, pre-trained on classification tasks, we demonstrate that our method consistently achieves substantial reductions in model size, with minimal impact on performance, and without the need for fine-tuning. Overall, our approach outperforms its counterparts, offering the best trade-off. Our code is available on GitHub.