Mining task offloading has been attracting users of decentralized applications (DApps) because they have only devices with the limited resource, which make it difficult to execute resource-intensive mining tasks. This allows the DApp users to offload the mining tasks to a cloud and/or a mobile edge computing server managed by a cloud service provider (CSP). To ensure the sustainable cloud/edge services and the integrity of blockchain, a CSP selection problem arises, which is a problem to assign the offloading requests to an appropriate CSP. In this paper, we propose a mining task offloading strategy for the CSP selection problem to maximize the miner’s expected utility. More specifically, we formulate the CSP selection problem as a repeated stochastic game such that the coarse correlated equilibrium is achieved among miners (DApp users). In addition, we develop an online algorithm for efficiently solving the repeated stochastic game using the Lyapunov optimization and the drift-plus-penalty algorithm. Through the numerical experiments, we demonstrate the characteristics of the proposed strategy in terms of parameter sensitivity, utility, fairness, and execution time.