With the remarkable development of the 5G technologies, more and more real-time and complex computational tasks from the Internet-of-Things (IoT) systems can be fulfilled by 5G edge servers. While the ultra-dense deployment is required for 5G edge services, in the upcoming era of 6G with an even more limited communication range, it is almost impossible to achieve 6G service coverage with dense deployments. To address this fundamental limit, we propose EdgeGO, a mobile resource-sharing framework that employs mobile edge servers to provide a cost-effective deployment of 6G edge computing, which enables edge resource sharing for massive IoT devices. Unlike traditional mobile cloudlets, EdgeGO exploits the asynchronization between requests receiving and results returning to decouple the stringent delay and resource requirements for edge computing. As a result, the server moving and task processing could be paralleled. Besides, EdgeGO incorporates a two-layer iterative updating algorithm, which jointly optimizes path planning and task scheduling to improve the overall task efficiency. Extensive simulation results show that, by careful managing mobility and task execution of the edge servers, EdgeGO is able to drastically increase the resource utilization by 166.67% and decrease the deployment cost of 6G edge computing by 25.58%.