Human tissue, which is inherently three-dimensional (3D), is traditionally examined through standard-of-care histopathology as limited two-dimensional (2D) cross-sections that can insufficiently represent the tissue due to sampling bias. To holistically characterize histomorphology, 3D imaging modalities have been developed, but clinical translation is hampered by complex manual evaluation and lack of computational platforms to distill clinical insights from large, high-resolution datasets. We present TriPath, a deep-learning platform for processing tissue volumes and efficiently predicting clinical outcomes based on 3D morphological features. Recurrence risk-stratification models were trained on prostate cancer specimens imaged with open-top light-sheet microscopy or microcomputed tomography. By comprehensively capturing 3D morphologies, 3D volume-based prognostication achieves superior performance to traditional 2D slice-based approaches, including clinical/histopathological baselines from six certified genitourinary pathologists. Incorporating greater tissue volume improves prognostic performance and mitigates risk prediction variability from sampling bias, further emphasizing the value of capturing larger extents of heterogeneous morphology.