As the fourth paradigm in materials research and development, materials genome engineering addresses the limitations inherent in traditional materials R&D models that rely on a “trial and error” approach. It improves the efficiency and quality of materials research and development. Leveraging the principles of materials genome engineering, this data-driven approach systematically correlates fundamental material characteristics—including chemical composition, microstructural features, and synthesis processes—with macroscopic mechanical properties. This paradigm facilitates the rational design and rapid development of advanced materials meeting stringent engineering demands. This paper reviews recent advances in predicting material mechanical properties from two key perspectives: machine learning and deep learning. Machine learning algorithms mainly include Random Forest, Gradient Boosting Decision Tree, K-Nearest Neighbors, Support Vector Regression. Deep learning algorithms mainly include multilayer perceptron machines, deep neural networks, and convolutional neural networks. We then survey the current predictive capabilities for key mechanical properties—including strength, toughness, plasticity, hardness, wear resistance, and fatigue life—in metallic, ceramic, and composite materials, as achieved by the aforementioned methods. The advantages and disadvantages of material property prediction methods are summarized and the future development direction of material mechanical property prediction is analyzed. This paper summarizes the present state of research and technological applications in predicting materials’ mechanical properties based on material genome engineering, aiding readers in gaining a swift understanding of developments within this field.