Thyroid nodule segmentation is a crucial step in the diagnostic procedure of physicians and computer-aided diagnosis systems. Mostly, current studies treat segmentation and diagnosis as independent tasks without considering the correlation between these tasks. The sequence steps of these independent tasks in computer-aided diagnosis systems may lead to the accumulation of errors. Therefore, it is worth combining them as a whole through exploring the relationship between thyroid nodule segmentation and diagnosis. According to the thyroid imaging reporting and data system (TI-RADS), the assessment of shape and margin characteristics is the prerequisite for the discrimination of benign and malignant thyroid nodules. These characteristics can be observed in the thyroid nodule segmentation masks. Inspired by the diagnostic procedure of TI-RADS, this paper proposes a shape-margin knowledge augmented network (SkaNet) for simultaneously thyroid nodule segmentation and diagnosis. Due to the similarity in visual features between segmentation and diagnosis, SkaNet shares visual features in the feature extraction stage and then utilizes a dual-branch architecture to perform thyroid nodule segmentation and diagnosis tasks simultaneously. To enhance effective discriminative features, an exponential mixture module is devised, which incorporates convolutional feature maps and self-attention maps by exponential weighting. Then, SkaNet is jointly optimized by a knowledge augmented multi-task loss function with a constraint penalty term. It embeds shape and margin characteristics through numerical computation and models the relationship between the thyroid nodule diagnosis results and segmentation masks.