Small Unmanned Aerial Vehicles (UAVs) are becoming potential threats to security-sensitive areas and personal privacy. A UAV can shoot photos at height, but how to detect such an uninvited intruder is an open problem. This paper presents mmHawkeye, a passive approach for UAV detection with a COTS millimeter wave (mmWave) radar. mmHawkeye doesn't require prior knowledge of the type, motions, and flight trajectory of the UAV, while exploiting the signal feature induced by the UAV's periodic micro-motion (PMM) for long-range accurate detection. The design is therefore effective in dealing with low-SNR and uncertain reflected signals from the UAV. mmHawkeye can further track the UAV's position with dynamic programming and particle filtering, and identify it with a Long Short-Term Memory (LSTM) based detector. We implement mmHawkeye on a commercial mmWave radar and evaluate its performance under varied settings. The experimental results show that mmHawkeye has a detection accuracy of 95.8% and can realize detection at a range up to 80m.