Underwater visual understanding has recently gained increasing attention within the computer vision community for studying and monitoring underwater ecosystems. Among these, coral reefs play an important and intricate role, often referred to as the rainforests of the sea, due to their rich biodiversity and crucial environmental impact. Existing coral analysis, due to its technical complexity, requires significant manual work from coral biologists, therefore hindering scalable and comprehensive studies. In this paper, we introduce CoralSCOP, the first foundation model designed for the automatic dense segmentation of coral reefs. CoralSCOP is developed to accurately assign labels to different coral entities, addressing the challenges in the semantic analysis of coral imagery. Its main objective is to identify and delineate the irregular boundaries between various coral individuals across different granularities, such as coral/non-coral, growth form, and genus. This task is challenging due to the semantic agnostic nature or fixed limited semantic categories of previous generic segmentation methods, which fail to adequately capture the complex characteristics of coral structures. By introducing a novel parallel semantic branch, CoralSCOP can produce high-quality coral masks with semantics that enable a wide range of downstream coral reef analysis tasks. We demonstrate that CoralSCOP exhibits a strong zero-shot ability to segment unseen coral images. To effectively train our foundation model, we propose CoralMask, a new dataset with 41,297 densely labeled coral images and 330,144 coral masks. We have conducted comprehensive and extensive experiments to demonstrate the advantages of CoralSCOP over existing generalist segmentation algorithms and coral reef analytical approaches.