Accurate polygonal building extraction requires not only region-level segmentation but also geometrically consistent vertex modeling. However, existing segment anything model (SAM)-based adaptations primarily optimize mask quality and lack explicit mechanisms for structured polygon prediction, leading to irregular contours and unstable vertex localization, especially under cross-domain scenarios. To address these limitations, we propose AsymSAM, an asymmetric feature-enhanced framework based on the SAM for polygonal building extraction. AsymSAM integrates an asymmetric hierarchical feature enhancement scheme and a hybrid fusion module in vanilla SAM. These components effectively leverage multilevel spatial and semantic information to enhance the representation of building contours and structural cues. Additionally, we extend the mask decoder to support joint prediction of polygon vertices and boundaries, enabling both automatic and prompt-guided extraction modes. Experiments on the WHU-Mix and SpaceNet datasets show AsymSAM consistently outperforms existing methods in terms of average precision (AP), average recall (AR), and intersection over union (IoU).