This paper presents the Global-Local Teleoperation Interface, a hierarchical framework that enhances human-robot interaction by decoupling large-scale manipulator positioning from fine end-effector manipulation. The global component enables efficient workspace traversal, while the local component facilitates precise and dexterous control. To address slave-side kinematic singularities-especially during fine manipulation, we propose a singularity-avoiding motion mapping strategy that enhances both stability and intuitiveness. We further introduce the concept of an operational Jacobian to characterize the smoothness of joint motion under local control. The G-L interface is implemented in two variants: Direct Mapping and Singularity-Avoiding Mapping, and is validated through hardware experiments involving precision tasks and complex motion. Results show substantial improvements in task success rate, efficiency, and user experience over conventional global or local-only systems.