Phase-field fracture (PFF) approach is highly effective in predicting complex crack patterns, including branching, merging, and fragmentation. However, addressing large-scale PFF problems, especially with non-adaptive models with dense meshes, involves high computational costs. While surrogate models offer a way to alleviate this bottleneck, the computational budget is still high for generating training data, particularly for large-scale PFF problems. This study addresses these challenges by developing an adaptive mesh refinement (AMR) enhanced sparse polynomial chaos expansion (PCE) framework for large-scale PFF problems. By incorporating AMR within the fracture analysis framework, we enhance computational efficiency in training data generation and eliminate the need for pre-refinement. A comparative study with four sparse solvers of sparse PCE is conducted to accurately relate domain input parameters to quantities of interest (QoIs) using a limited set of training data. Similarly, a relative comparison of the predicted load-displacement relationships are observed with these sparse solvers. A computationally expensive benchmark test reveals the relative precision of the proposed method with different solvers along with the computational efficiency compared to the well-known AMR method, representing a considerable advancement in fracture mechanics.