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Prostate cancer metastasis to bone and lymph nodes marks a critical transition to incurable disease, with five-year survival dropping dramatically compared to localized disease. Early identification of patients at high risk of metastasis enables timely intensification of treatment, including androgen deprivation therapy, salvage radiation, or systemic therapies. Current deep survival models that integrate serial PSA measurements and genomic risk scores achieve high predictive accuracy for time-to-metastasis but operate as black boxes, providing no explanation for why a particular patient is predicted to have early or late metastasis. Clinicians cannot trust or act upon predictions without understanding which PSA features or genomic markers drive the risk assessment. We present an explainable deep survival framework that combines a deep survival model for time-to-metastasis prediction with Integrated Gradients attribution, a method that distributes the model's hazard prediction among input features. The framework produces patient-specific explanations showing how each serial PSA value and each genomic score component contributes to the predicted metastasis hazard. The framework consists of three core components: (1) a deep survival model (DeepSurv architecture) with a PSA time-series encoder and genomic risk encoder, (2) Integrated Gradients attribution computed over the hazard function, and (3) visualization tools for individual and population-level interpretations. Integrated Gradients attributes the predicted hazard to individual PSA measurements across time and specific genomic markers, enabling clinicians to distinguish between risk driven by rapid PSA kinetics versus high genomic risk scores. This interpretability transforms a black-box survival prediction into an actionable clinical decision support tool.