Aneurysm segmentation in computed tomography angiography (CTA) images is essential for medical intervention aimed at preventing subarachnoid hemorrhages. However, most existing studies tend to overlook the topological characteristics of arteries related to aneurysms, often resulting in suboptimal performance in aneurysm segmentation. To address this challenge, we propose an artery-aware global-to-local framework for aneurysm segmentation (AASeg) using CTA images of head and neck. This framework consists of two key components: 1) a centerline graph network (CG-Net) for aneurysm global localization, and 2) a point cloud network (PC-Net) for local aneurysm segmentation. The centerline graph is generated by extracting artery centerline structures from vessel masks obtained through a pre-trained model for head and neck vessel segmentation. This representation serves as a high-level representation of the artery structure, allowing for analysis of aneurysms along the entire arteries. It facilitates aneurysm localization via aneurysm-segment graph classification along the arteries. Then, local region of aneurysm segment can be sampled from the vessel mask according to the aneurysm-segment graph. Subsequently, aneurysm segmentation is performed on the point cloud constructed from the aneurysm segment through the PC-Net. Extensive experiments show that the proposed framework achieves state-of-the-art performance in aneurysm localization on a main dataset and an external testing dataset, with Recall of 84.1% and 80.7%, false positives per case of 1.72 and 1.69, and segmentation DSC of 66.1% and 60.2%, respectively.