Cancer is mainly caused by somatic genome alterations (SGAs). Precision oncology involves identifying and targeting tumor-specific aberrations resulting from causative SGAs. We developed a novel tumor-specific computational framework that finds the likely causative SGAs in an individual tumor and estimates their impact on oncogenic processes, which suggests the disease mechanisms that are acting in that tumor. This information can be used to guide precision oncology. We report a tumor-specific causal inference (TCI) framework, which estimates causative SGAs by modeling causal relationships between SGAs and molecular phenotypes (e.g., transcriptomic, proteomic, or metabolomic changes) within an individual tumor. We applied the TCI algorithm to tumors from The Cancer Genome Atlas (TCGA) and estimated for each tumor the SGAs that causally regulate the differentially expressed genes (DEGs) in that tumor. Overall, TCI identified 634 SGAs that are predicted to cause cancer-related DEGs in a significant number of tumors, including most of the previously known drivers and many novel candidate cancer drivers. The inferred causal relationships are statistically robust and biologically sensible, and multiple lines of experimental evidence support the predicted functional impact of both the well-known and the novel candidate drivers that are predicted by TCI. TCI provides a unified framework that integrates multiple types of SGAs and molecular phenotypes to estimate which genome perturbations are causally influencing one or more molecular/cellular phenotypes in an individual tumor. By identifying major candidate drivers and revealing their functional impact in an individual tumor, TCI sheds light on the disease mechanisms of that tumor, which can serve to advance our basic knowledge of cancer biology and to support precision oncology that provides tailored treatment of individual tumors.