The state-of-art DNN structures involve intensive computation and high memory storage. To mitigate the challenges, the memristor crossbar array has emerged as an intrinsically suitable matrix computation and low-power acceleration framework for DNN applications. However, the high accuracy solution for extreme model compression on memristor crossbar array architecture is still waiting for unraveling. In this paper, we propose a memristor-based DNN framework which combines both structured weight pruning and quantization by incorporating alternating direction method of multipliers (ADMM) algorithm for better pruning and quantization performance. We also discover the non-optimality of the ADMM solution in weight pruning and the unused data path in a structured pruned model. Motivated by these discoveries, we design a software-hardware co-optimization framework which contains the first proposed Network Purification and Unused Path Removal algorithms targeting on post-processing a structured pruned model after ADMM steps. By taking memristor hardware constraints into our whole framework, we achieve extreme high compression ratio on the state-of-art neural network structures with minimum accuracy loss. For quantizing structured pruned model, our framework achieves nearly no accuracy loss after quantizing weights to 8-bit memristor weight representation. We share our models at anonymous link https://bit.ly/2VnMUy0.