Semantic-based test generators are widely used to produce failure-inducing inputs for Deep Learning (DL) systems. They typically generate challenging test inputs by applying random perturbations to input semantic concepts until a failure is found or a timeout is reached. However, such randomness may hinder them from efficiently achieving their goal. This paper proposes XMutant, a technique that leverages explainable artificial intelligence (XAI) techniques to generate challenging test inputs. XMutant uses the local explanation of the input to inform the fuzz testing process and effectively guide it toward failures of the DL system under test. We evaluated different configurations of XMutant in triggering failures for different DL systems both for model-level (sentiment analysis, digit recognition) and system-level testing (advanced driving assistance). Our studies showed that XMutant enables more effective and efficient test generation by focusing on the most impactful parts of the input. XMutant generates up to 125% more failure-inducing inputs compared to an existing baseline, up to 7X faster. We also assessed the validity of these inputs, maintaining a validation rate above 89%, according to automated and human validators.