Due to the strong reliance on domain-specific knowledge, the joint learning manner of domain discrimination and translation has been widely considered in the Multi-Domain Neural Machine Translation (MDNMT) task. However, the word ambiguity problem still inevitably exists in MDNMT, especially when mixed multi-domain data is brought into the model training phase. Although word-level MDNMT can mitigate this problem to some extent, poor domain discrimination yet remains and severely hinders performance. Based on the above limitation, we observed that coarser granularity strings may provide more specific semantics, which is more conducive to domain discrimination. Thus, we propose a Word-level Domain-Sensitive Representation Learning (WDSRL) method. Specifically, we focus on two aspects of our approach: domain representation and domain discrimination. To extend the scope of domain representation, we adopt Convolution Neural Networks (CNN) to encode Local Domain Representation at different granularities, and then integrate Topic Knowledge Representation into each word. By doing so, context features related to the domain could be comprehensively enriched. Regarding domain discrimination, we design a Domain-Sensitive Discriminator, which could not only generate domain features for each word but also enhance domain representation learning. Experimental results demonstrate our substantial improvements over several representative baselines on multiple language pairs. Furthermore, the extensive analysis also indicates the superiority of our proposed domain-sensitive feature encoding strategy and domain-sensitive discriminator for word-level representation learning.