The sixth-generation (6G) system is widely envisioned as a global network consisting of pervasive devices that interact with each other. Besides exchanging information, these peer entities also share heterogeneous and distributed edge resources. Blockchain is a promising technology to secure resource sharing in a peer-to-peer way. However, constrained by limited transaction throughput, existing blockchain systems (e.g., Bitcoin) cannot process numerous resource transactions concurrently produced in large-scale 6G networks. To cope with this issue, we propose a blockchain scaling scheme that combines Directed Acyclic Graph (DAG) with sharding. Our sharding method divides blockchain transactions into multiple mutually disjoint subsets maintained by different committees, which enables high-volume resource transactions to be processed and recorded concurrently. Additionally, all committees maintain a global DAG of blocks to resolve the security degradation raised by the sharding method. Moreover, we put forth a computation efficient consensus algorithm by leveraging miners' computing power to improve resource utilization efficiency. Numerical results show that the proposed scheme achieves good performance in resource utilization efficiency.