Surface roughness is a key indicator of product quality, and developing a precise prediction model contributes to optimizing processes and enhancing production efficiency. Current models for predicting surface roughness primarily include theoretical and data-driven models. However, due to the complex nature of the grinding process, theoretical models that rely on simplified assumptions often fail to estimate surface roughness accurately. Additionally, data-driven models lack physical interpretation and exhibit a high dependence on data, which limits their practical application. To address these issues, this paper proposes a novel physics-guided cascade model for predicting surface roughness in grinding. Firstly, a theoretical model is established based on machining theory, which estimates surface roughness by analyzing the material removal process and surface formation mechanism. Subsequently, the theoretical model predictions are utilized as prior knowledge and combined with grinding process parameters to perform secondary modeling using a regularized extreme learning machine (RELM), capturing hidden information that may be overlooked by the theoretical model. The effectiveness of the proposed cascade model is validated through robotic grinding experiments conducted under various conditions. Compared to traditional benchmark methods, the proposed model demonstrates significant improvements in both accuracy and interpretability while also exhibiting robust performance with smaller-scale datasets. By integrating physical insights with data-driven modeling, the proposed cascade model offers a practical solution to the limitations of existing approaches and holds promise for broader applications in automated processes.