In this paper, a novel framework that uses wireless mobile miners (MMs) for computation purposes in a blockchain system is proposed. In the introduced system, the blockchain ledger is located at the communication nodes (CNs), and the MMs associated with CNs process the blockchain's proof-of-work (PoW) computation to verify the originality of the data. The MM that is the first to finish its PoW will receive a reward by sending its computing result to the CNs that are connected to other MMs. In the considered scenario, a blockchain forking event occurs if the MM having the shortest PoW delay fails to be the first to update its computing result to other MMs. To enable such mobile operations for a blockchain with minimum forking events, it is imperative to maintain low-latency wireless communications between MMs and CNs. To analyze the sensitivity of the system to latency, the probability of occurrence of a forking event is theoretically derived. The system is then designed so as to compute the forked block's PoW again to recover from a forking event. For this case, the average energy consumption of an MM is derived as a function of the system parameters such as the number of MMs and power consumed by the computing, transmission, and mobility processes of the MMs. Simulation results verify the analytical derivations and show that using a larger number of MMs can reduce the energy consumption by up to 94.5% compared to a blockchain system with a single MM.