Volume Projection Imaging from ultrasound data is a promising technique to visualize spine features and diagnose Adolescent Idiopathic Scoliosis. In this paper, we present a novel multi-task framework to reduce the scan noise in volume projection images and to segment different spine features simultaneously, which provides an appealing alternative for intelligent scoliosis assessment in clinical applications. Our proposed framework consists of two streams: i) A noise removal stream based on generative adversarial networks, which aims to achieve effective scan noise removal in a weakly-supervised manner, i.e., without paired noisy-clean samples for learning; ii) A spine segmentation stream, which aims to predict accurate bone masks. To establish the interaction between these two tasks, we propose a selective feature-sharing strategy to transfer only the beneficial features, while filtering out the useless or harmful information. We evaluate our proposed framework on both scan noise removal and spine segmentation tasks. The experimental results demonstrate that our proposed method achieves promising performance on both tasks, which provides an appealing approach to facilitating clinical diagnosis.