Elasticity is highly desirable for stream processing systems to guarantee low latency against workload dynamics, such as surges in data arrival rate and fluctuations in data distribution. Existing systems achieve elasticity following a resource-centric approach that uses dynamic key partitioning across the parallel instances, i.e. executors, to balance the workload and scale operators. However, such operator-level key repartitioning needs global synchronization and prohibits rapid elasticity. To address this problem, we propose an executor-centric approach, whose core idea is to avoid operator-level key repartitioning while implementing each executor as the building block of elasticity. Following this new approach, we design the Elasticutor framework with two level of optimizations: i) a novel implementation of executors, i.e., elastic executors, that perform elastic multi-core execution via efficient intra-executor load balancing and executor scaling and ii) a global model-based scheduler that dynamically allocates CPU cores to executors based on the instantaneous workloads. We implemented a prototype of Elasticutor and conducted extensive experiments. Our results show that Elasticutor doubles the throughput and achieves an average processing latency up to 2 orders of magnitude lower than previous methods, for a dynamic workload of real-world applications.