Automatic detection of cervical lesion cells or cell clumps using cervical cytology images is critical to computer-aided diagnosis (CAD) for accurate, objective, and efficient cervical cancer screening. Recently, many methods based on modern object detectors were proposed and showed great potential for automatic cervical lesion detection. Although effective, several issues still hinder further performance improvement of such known methods, such as large appearance variances between single-cell and multi-cell lesion regions, neglecting normal cells, and visual similarity among abnormal cells. To tackle these issues, we propose a new task decomposing and cell comparing network, called TDCC-Net, for cervical lesion cell detection. Specifically, our task decomposing scheme decomposes the original detection task into two subtasks and models them separately, which aims to learn more efficient and useful feature representations for specific cell structures and then improve the detection performance of the original task. Our cell comparing scheme imitates clinical diagnosis of experts and performs cell comparison with a dynamic comparing module (normal-abnormal cells comparing) and an instance contrastive loss (abnormal-abnormal cells comparing). Comprehensive experiments on a large cervical cytology image dataset confirm the superiority of our method over state-of-the-art methods.