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While progress has been made on the visual question answering leaderboards, models often utilize spurious correlations and priors in datasets under the i.i.d. setting. As such, evaluation on out-of-distribution (OOD) test samples has emerged as a proxy for generalization. In this paper, we present MUTANT, a training paradigm that exposes the model to perceptually similar, yet semantically distinct mutations of the input, to improve OOD generalization, such as the VQA-CP challenge. Under this paradigm, models utilize a consistency-constrained training objective to understand the effect of semantic changes in input (question-image pair) on the output (answer). Unlike existing methods on VQA-CP, MUTANT does not rely on the knowledge about the nature of train and test answer distributions. MUTANT establishes a new state-of-the-art accuracy on VQA-CP with a improvement. Our work opens up avenues for the use of semantic input mutations for OOD generalization in question answering.