Accelerating DNN execution on resource-limited computing platforms has been a long-standing problem. Prior works utilize l1-based group lasso or dynamic regularization such as ADMM to perform structured pruning on DNN models to leverage the parallel computing architectures. However, both of the pruning schemes and pruning methods lack universality, which leads to degraded performance and limited applicability. Considering mobile devices are becoming an important carrier for deep learning tasks, current approaches are not ideal for fully exploiting mobile parallelism while achieving high inference accuracy. To solve the problem, we propose BLCR, a novel block-based pruning framework that comprises a general and flexible structured pruning scheme that enjoys higher flexibility while exploiting full on-device parallelism, as well as a powerful and efficient reweighted regularization method to achieve the proposed sparsity scheme. Our framework is universal, which can be applied to both CNNs and RNNs, implying complete support for the two major kinds of computation-intensive layers (i.e., CONV and FC layers). To complete all aspects of the pruning-for-acceleration task, we also integrate compiler-based code optimization into our framework that can perform DNN inference on mobile devices in real-time. To the best of our knowledge, it is the first time that the weight pruning framework achieves universal coverage for both CNNs and RNNs with real-time mobile acceleration and no accuracy compromise.