In the studies of self-adaptive systems (SAS), requirement relaxation is a widely discussed approach for managing the system's requirements when dealing with the runtime environment changes (e.g., ignoring low-priority requirements to guarantee high-priority requirements). Guaranteeable requirement analysis (GRA) is recently proposed to determine the relaxation by checking the feasibility of all requirement combinations, enabling the SAS to realize the relaxation autonomously. However, a critical problem of GRA is the trade-off between analysis/relaxation precision and computation time at different granularity levels of requirements. Specifically, the analysis may not be precise enough if the requirements are coarse-grained (i.e., high granularity level), while the analysis may take a too long time if the requirements are fine-grained (i.e., low granularity level). This paper proposed a method, namely iterative adaptation via multi-grained requirement relaxation, to achieve the advantages of high precision and short computation time. Specifically, the SAS first deploys a rapid (but imprecise) relaxation using high granularity-level requirements. It then repeatedly iterates to a preciser (but slower) relaxation with a progressive decrease in the granularity level. An experiment based on the warehouse robot system demonstrates the validity of our proposal.