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Recently, variational auto-encoder (VAE) based approaches have made impressive progress on improving the diversity of generated responses. However, these methods usually suffer the cost of decreased relevance accompanied by diversity improvements. In this paper, we propose a novel multimodal response generation framework with exemplar augmentation and curriculum optimization to enhance relevance and diversity of generated responses. First, unlike existing VAE-based models that usually approximate a simple Gaussian posterior distribution, we present a Gaussian mixture posterior distribution (i.e, multimodal) to further boost response diversity, which helps capture complex semantics of responses. Then, to ensure that relevance does not decrease while diversity increases, we fully exploit similar examples (exemplars) retrieved from the training data into posterior distribution modeling to augment response relevance. Furthermore, to facilitate the convergence of Gaussian mixture prior and posterior distributions, we devise a curriculum optimization strategy to progressively train the model under multiple training criteria from easy to hard. Experimental results on widely used SwitchBoard and DailyDialog datasets demonstrate that our model achieves significant improvements compared to strong baselines in terms of diversity and relevance.