The Transformer has been an indispensable staple in deep learning. However, for real-life applications, it is very challenging to deploy efficient Transformers due to immense parameters and operations of models. To relieve this burden, exploiting sparsity is an effective approach to accelerate Transformers. Newly emerging Ampere GPUs leverage a 2:4 sparsity pattern to achieve model acceleration, while it can hardly meet the diverse algorithm and hardware constraints when deploying models. By contrast, we propose an algorithm-hardware co-optimized framework to flexibly and efficiently accelerate Transformers by utilizing general N:M sparsity patterns. (1) From algorithm perspective, we propose a sparsity inheritance mechanism along with an inherited dynamic pruning (IDP) method to obtain a series of N:M sparse candidate Transformers rapidly. A model compression scheme is further proposed to significantly reduce the storage requirement for deployment. (2) From hardware perspective, we present a flexible and efficient hardware architecture, namely STA, to achieve significant speedup when deploying N:M sparse Transformers. STA features not only a computing engine unifying both sparse-dense and dense-dense matrix multiplications with high computational efficiency but also a scalable softmax module eliminating the latency from intermediate off-chip data communication. Experimental results show that compared to other methods, N:M sparse Transformers, generated using IDP, achieves an average of 6.7% improvement on accuracy with high training efficiency. Moreover, STA can achieve 14.47x and 11.33x speedup compared to Intel i9-9900X and NVIDIA RTX 2080 Ti, respectively, and perform 2.00-19.47x faster inference than the state-of-the-art FPGA-based accelerators for Transformers.