Online data services have stringent performance requirement and must tolerate workload fluctuation. This paper introduces Pitstop, a new query language runtime design built on the idea of \emph{interruptible query processing}: the time-consuming task of data inspection for processing each query or update may be interrupted and resumed later at the boundary of fine-grained data partitions. This counter-intuitive idea enables a novel form of \emph{fine-grained concurrency} while preserving \emph{sequential consistency}. We build Pitstop through modifying the language runtime of Cypher, the query language of a state-of-the-art graph database, Neo4j. Our evaluation on the Google Cloud shows that Pitstop can outperform unmodified Neo4j during workload fluctuation, with reduced latency and increased throughput.