Contrastive Learning (CL) is one of the most popular self-supervised learning frameworks for graph representation learning, which trains a Graph Neural Network (GNN) by discriminating positive and negative node pairs. However, there are two challenges for CL on graphs. On the one hand, traditional CL methods will unavoidably introduce semantic errors since they will treat some semantically similar nodes as negative pairs. On the other hand, most of the existing CL methods ignore the multiplexity nature of the real-world graphs, where nodes are connected by various relations and each relation represents a view of the graph. To address these challenges, we propose a novel Graph Multi-View Prototypical (Graph-MVP) framework to extract node embeddings on multiplex graphs. Firstly, we introduce a Graph Prototypical Contrastive Learning (Graph-PCL) framework to capture both node-level and semantic-level information for each view of multiplex graphs. Graph-PCL captures the node-level information by a simple yet effective data transformation technique. It captures the semantic-level information by an Expectation-Maximization (EM) algorithm, which alternatively performs clustering over node embeddings and parameter updating for GNN. Next, we introduce Graph-MVP based on Graph-PCL to jointly model different views of the multiplex graphs. Our key insight behind Graph-MVP is that different view-specific embeddings of the same node should have similar underlying semantic, based on which we propose two versions of Graph-MVP: Graph-MVP_hard and Graph-MVP_soft to align embeddings across views. Finally, we evaluate the proposed Graph-PCL and Graph-MVP on a variety of real-world datasets and downstream tasks. The experimental results demonstrate the effectiveness of the proposed Graph-PCL and Graph-MVP frameworks.