Risk-averse distributionally robust multi-item newsvendor problems provide a fundamental model for inventory decisions under demand uncertainty, limited distributional information, and downside-risk concerns. We study this problem under mean-covariance demand ambiguity, where the decision maker maximizes the worst-case conditional value-at-risk of profit. While cross-item demand correlations are important for portfolio-level inventory decisions, they are difficult to estimate reliably in high dimensions. Moreover, preserving the full covariance information leads to an NP-hard formulation that is computationally challenging for large assortments. We develop a lifting-and-splitting framework that combines exact reformulation, scalable approximation, and performance guarantees. First, we derive an exact semidefinite programming reformulation based on the constrained Boolean quadric polytope, replacing exponentially many positive semidefinite constraints in the classical dual formulation with exponentially many linear constraints. Second, we propose a correlation-splitting approximation that partitions items into clusters, preserves within-cluster covariance information, and relaxes cross-cluster dependence. We establish exactness conditions and derive an explicit cluster-wise upper bound on the optimality gap. We further show that, in the two-cluster case, the approximation becomes increasingly accurate when one cluster has uniformly small demand variability, motivating a simple variance-based splitting rule. Numerical experiments demonstrate improved exact-solution tractability, strong approximation quality, and scalability to large instances.