Smart manufacturing in the context of Industry 4.0 presents new characteristics, such as large-scale, complex sub-processes cooperation, and integrated information management, which makes comprehensive performance-driven process monitoring difficult to be achieved in practice. Cloud–edge-device collaboration brings new perspectives for modern industries. This paper presents a performance-driven process monitoring framework in cloud–edge-device collaborative architecture, including a spatio-temporal information analytics based method and its application to a hot strip mill process (HSMP). Firstly, an integrated performance-driven process monitoring framework is proposed, where different monitoring tasks are deployed in the device, edge, and cloud layers, respectively. Secondly, a new performance-related spatio-temporal information analytics based fault detection and localization method is developed. In detail, temporal kernel canonical correlation analysis (CCA) is employed to extract the canonical correlation features with nonlinearities in the temporal domains, and spatial CCA is designed to form the spatial features. Based on the spatio-temporal features, the equipment operation condition monitoring model is developed in the device layer for real-time fault localization, and the process monitoring model is deployed in the edge for fault detection. Furthermore, to give a high-level evaluation of the operating status of the process, a qualitative trend analysis based operation risks evaluation model is deployed in the cloud. Different from the traditional architectures, the data processing capability of each layer is fully utilized in the proposed one, and the function is relevant to the enterprise management system. It provides a topological basis with clear priorities for subsequent process regulation and optimization. Finally, an actual HSMP is introduced to testify the performance of the framework. From the results, the fault detection rates are improved in comparison with traditional methods, and the fault localization results are consistent with the actual situations.