Deep neural networks (DNNs) are nowadays witnessing a major success in solving many pattern recognition tasks including skeleton-based classification. The deployment of DNNs on edge-devices, endowed with limited time and memory resources, requires designing lightweight and efficient variants of these networks. Pruning is one of the lightweight network design techniques that operate by removing unnecessary network parts, in a structured or an unstructured manner, including individual weights, neurons or even entire channels. Nonetheless, structured and unstructured pruning methods, when applied separately, may either be inefficient or ineffective.In this paper, we devise a novel semi-structured method that discards the downsides of structured and unstructured pruning while gathering their upsides to some extent. The proposed solution is based on a differentiable cascaded parametrization which combines (i) a band-stop mechanism that prunes weights depending on their magnitudes, (ii) a weight-sharing parametrization that prunes connections either individually or group-wise, and (iii) a gating mechanism which arbitrates between different group-wise and entry-wise pruning. All these cascaded parametrizations are built upon a common latent tensor which is trained end-to-end by minimizing a classification loss and a surrogate tensor rank regularizer. Extensive experiments, conducted on the challenging tasks of action and hand-gesture recognition, show the clear advantage of our proposed semi-structured pruning approach against both structured and unstructured pruning, when taken separately, as well as the related work.