Cross-lingual representation learning transfers knowledge from resource-rich data to resource-scarce ones to improve the semantic understanding abilities of different languages. However, previous works rely on shallow unsupervised data generated by token surface matching, regardless of the global context-aware semantics of the surrounding text tokens. In this paper, we propose an Unsupervised Pseudo Semantic Data Augmentation (UniPSDA) mechanism for cross-lingual natural language understanding to enrich the training data without human interventions. Specifically, to retrieve the tokens with similar meanings for the semantic data augmentation across different languages, we propose a sequential clustering process in 3 stages: within a single language, across multiple languages of a language family, and across languages from multiple language families. Meanwhile, considering the multi-lingual knowledge infusion with context-aware semantics while alleviating computation burden, we directly replace the key constituents of the sentences with the above-learned multi-lingual family knowledge, viewed as pseudo-semantic. The infusion process is further optimized via three de-biasing techniques without introducing any neural parameters. Extensive experiments demonstrate that our model consistently improves the performance on general zero-shot cross-lingual natural language understanding tasks, including sequence classification, information extraction, and question answering.