Accurate interpretation of knee MRI scans relies on expert clinical judgment, often with high variability and limited scalability. Existing radiomic approaches use a fixed set of radiomic features (the signature), selected at the population level and applied uniformly to all patients. While interpretable, these signatures are often too constrained to represent individual pathological variations. As a result, conventional radiomic-based approaches are found to be limited in performance, compared with recent end-to-end deep learning (DL) alternatives without using interpretable radiomic features. We argue that the individual-agnostic nature in current radiomic selection is not central to its intepretability, but is responsible for the poor generalization in our application. Here, we propose a novel radiomic fingerprint framework, in which a radiomic feature set (the fingerprint) is dynamically constructed for each patient, selected by a DL model. Unlike the existing radiomic signatures, our fingerprints are derived on a per-patient basis by predicting the feature relevance in a large radiomic feature pool, and selecting only those that are predictive of clinical conditions for individual patients. The radiomic-selecting model is trained simultaneously with a low-dimensional (considered relatively explainable) logistic regression for downstream classification. We validate our methods across multiple diagnostic tasks including general knee abnormalities, anterior cruciate ligament (ACL) tears, and meniscus tears, demonstrating comparable or superior diagnostic accuracy relative to state-of-the-art end-to-end DL models. More importantly, we show that the interpretability inherent in our approach facilitates meaningful clinical insights and potential biomarker discovery, with detailed discussion, quantitative and qualitative analysis of real-world clinical cases to evidence these advantages.