Information systems support the execution of business processes. The event logs of these executions generally contain sensitive information about customers, patients, and employees. The corresponding privacy challenges can be addressed by anonymizing the event logs while still retaining utility for process discovery. However, trading off utility and privacy is difficult: the higher the complexity of event log, the higher the loss of utility by anonymization. In this work, we propose a pipeline that combines anonymization and event data partitioning, where event abstraction is utilized for partitioning. By leveraging event abstraction, event logs can be segmented into multiple parts, allowing each sub-log to be anonymized separately. This pipeline preserves privacy while mitigating the loss of utility. To validate our approach, we study the impact of event partitioning on two anonymization techniques using three real-world event logs and two process discovery techniques. Our results demonstrate that event partitioning can bring improvements in process discovery utility for directly-follows-based anonymization techniques.