In modern recommender systems, sequential recommendation leverages chronological user behaviors to make effective next-item suggestions, which suffers from data sparsity issues, especially for new users. One promising line of work is the cross-domain recommendation, which trains models with data across multiple domains to improve the performance in data-scarce domains. Recent proposed cross-domain sequential recommendation models such as PiNet and DASL have a common drawback relying heavily on overlapped users in different domains, which limits their usage in practical recommender systems. In this paper, we propose a Mixed Attention Network (MAN) with local and global attention modules to extract the domain-specific and cross-domain information. Firstly, we propose a local/global encoding layer to capture the domain-specific/cross-domain sequential pattern. Then we propose a mixed attention layer with item similarity attention, sequence-fusion attention, and group-prototype attention to capture the local/global item similarity, fuse the local/global item sequence, and extract the user groups across different domains, respectively. Finally, we propose a local/global prediction layer to further evolve and combine the domain-specific and cross-domain interests. Experimental results on two real-world datasets (each with two domains) demonstrate the superiority of our proposed model. Further study also illustrates that our proposed method and components are model-agnostic and effective, respectively. The code and data are available at https://github.com/Guanyu-Lin/MAN.