The operation and maintenance (O&M) of database systems is critical to ensuring system availability and performance, typically requiring expert experience (e.g., identifying metric-to-anomaly relations) for effective diagnosis and recovery. However, existing automatic database O&M methods, including commercial products, cannot effectively utilize expert experience. On the one hand, rule-based methods only support basic O&M tasks (e.g., metric-based anomaly detection), which are mostly numerical equations and cannot effectively incorporate literal O&M experience (e.g., troubleshooting guidance in manuals). On the other hand, LLM-based methods, which retrieve fragmented information (e.g., standard documents + RAG), often generate inaccurate or generic results. To address these limitations, we present DBAIOps, a novel hybrid database O&M system that combines reasoning LLMs with knowledge graphs to achieve DBA-style diagnosis. First, DBAIOps introduces a heterogeneous graph model for representing the diagnosis experience, and proposes a semi-automatic graph construction algorithm to build that graph from thousands of documents. Second, DBAIOps develops a collection of (800+) reusable anomaly models that identify both directly alerted metrics and implicitly correlated experience and metrics. Third, for each anomaly, DBAIOps proposes a two-stage graph evolution mechanism to explore relevant diagnosis paths and identify missing relations automatically. It then leverages a reasoning LLM (e.g., DeepSeek-R1) to infer root causes and generate clear diagnosis reports for both DBAs and common users. Our evaluation over four mainstream database systems (Oracle, MySQL, PostgreSQL, and DM8) demonstrates that DBAIOps outperforms state-of-the-art baselines, 34.85% and 47.22% higher in root cause and human evaluation accuracy, respectively.