Contact-rich manipulation tasks in unstructured environments pose significant robustness challenges for robot learning, where unexpected collisions can cause damage and hinder policy acquisition. Existing soft end-effectors face fundamental limitations: they either provide a limited deformation range, lack directional stiffness control, or require complex actuation systems that compromise practicality. This study introduces CLAW (Compliant Leaf-spring Anisotropic soft Wrist), a novel soft wrist mechanism that addresses these limitations through a simple yet effective design using two orthogonal leaf springs and rotary joints with a locking mechanism. CLAW provides large 6-degree-of-freedom deformation (40mm lateral, 20mm vertical), anisotropic stiffness that is tunable across three distinct modes, while maintaining lightweight construction (330g) at low cost ($550). Experimental evaluations using imitation learning demonstrate that CLAW achieves 76% success rate in benchmark peg-insertion tasks, outperforming both the Fin Ray gripper (43%) and rigid gripper alternatives (36%). CLAW successfully handles diverse contact-rich scenarios, including precision assembly with tight tolerances and delicate object manipulation, demonstrating its potential to enable robust robot learning in contact-rich domains. Project page: https://project-page-manager.github.io/CLAW/