Genome-wide analysis, which provides perceptive insights into complex diseases, plays an important role in biomedical data analytics. It usually involves large-scale human genomic data, and thus may disclose sensitive information about individuals. While existing studies have been conducted against data exfiltration by external malicious actors, this work focuses on the emerging identity tracing attack that occurs when a dishonest insider attempts to re-identify obtained DNA samples. We propose a framework named υFRAG to facilitate privacy-preserving data sharing and computation in genome-wide analysis. υFRAG mitigates privacy risks by using vertical fragmentations to disrupt the genetic architecture on which the adversary relies for re-identification. The fragmentation significantly reduces the overall amount of information the adversary can obtain. Notably, it introduces no sacrifice to the capability of genome-wide analysis—we prove that it preserves the correctness of gradient descent, the most popular optimization approach for training machine learning models. We also explore the efficiency performance of υFRAG through experiments on a large-scale, real-world dataset. Our experiments demonstrate that υFRAG outperforms not only secure multiparty computation (MPC) and homomorphic encryption (HE) protocols with a speedup of more than 221x for training neural networks, but also noise-based differential privacy (DP) solutions and traditional non-private algorithms in most settings.