In laser welding, the complex characteristics of weld structure features, including weld geometry and defects such as porosities and cracks, pose significant challenges in analyzing the relationship between weld structure and mechanical performance. This study tackles this issue by introducing a data-driven approach to quantify the significance of specific weld structure features and their correlation with mechanical performance in laser-welded aluminum-copper thin sheets. High-resolution, three-dimensional micro-X-ray tomography provides detailed characterization of weld structure features, including weld geometry and defect attributes. Advanced deep learning techniques and interpretable machine learning models are employed to analyze weld geometry and defect features with precision. Importance analysis identifies a strong correlation between weld geometry and fracture behavior. Further investigation demonstrates that weld geometry exerts a significant influence on other structural features, such as porosity and crack characteristics, highlighting its critical role in predicting fracture behavior. To improve predictions of fracture mode, a novel dimensionless failure mode index is proposed and validated using data from this study and existing literature. This index establishes a robust relationship between weld geometry, defect features, and fracture modes, offering a practical and reliable tool for evaluating weld performance.