Attentional models are distinctly characterized by their ability to learn relative importance, i.e., assigning a different weight to input values. This paper proposes a new quasi-attention that is compositional in nature, i.e., learning whether to \textit{add}, \textit{subtract} or \textit{nullify} a certain vector when learning representations. This is strongly contrasted with vanilla attention, which simply re-weights input tokens. Our proposed \textit{Compositional De-Attention} (CoDA) is fundamentally built upon the intuition of both similarity and dissimilarity (negative affinity) when computing affinity scores, benefiting from a greater extent of expressiveness. We evaluate CoDA on six NLP tasks, i.e. open domain question answering, retrieval/ranking, natural language inference, machine translation, sentiment analysis and text2code generation. We obtain promising experimental results, achieving state-of-the-art performance on several tasks/datasets.