Edge and Mist Computing are two emerging paradigms that aim to reduce latency and the Cloud workload by bringing its applications close to the Internet of Things (IoT) devices. In such complex environments, simulation makes it possible to evaluate the adopted strategies before their deployment on a real distributed system. However, despite the research advancement in this area, simulation tools are lacking, especially in the case of Mist Computing [11], where heterogeneous and constrained devices cooperate and share their resources. Motivated by this, in this paper, we present PureEdgeSim, a simulation toolkit that enables the simulation of Cloud, Edge, and Mist Computing environments and the evaluation of the adopted resources management strategies, in terms of delays, energy consumption, resources utilization, and tasks success rate. To show its capabilities, we introduce a case study, in which we evaluate the different architectures, orchestration algorithms, and the impact of offloading criteria. The simulation results show the effectiveness of PureEdgeSim in modeling such complex and dynamic environments.