In the context of smart manufacturing, modern industrial processes are becoming increasingly complex in terms of process flows, product varieties, and performance indicators (PIs). Performance-driven process monitoring attracts extensive attentions in recent years. However, most methods require spatio-temporal correspondence between process variables and PIs, and rarely consider the correlation among various PIs. In this paper, a spatio-temporal feature extraction network-based multi-performance indicators synergetic monitoring framework is presented. Firstly, considering the missing data in PI measurements, a weighted sum of tensor nuclear norm (WSTNN) based batch-process data completion approach is developed, which can adeptly handle local missing and incomplete data issues and establish the spatio-temporal correspondence for subsequent modeling. Secondly, for a specific PI, a new canonical variate analysis embedded spatio-temporal convolutional network (CVA-STCN) is designed to extract the PI-related features with spatio-temporal dependency. Thirdly, considering the dynamic interaction of multiple PIs, a third-order feature tensor is established to perform the future fusion, and the correlations among various PI-related features are explored via tensor decomposition. Finally, a hierarchical multi-performance indicators synergetic monitoring model is developed over several subspaces. The proposed method is verified on Tennessee Eastman process and an actual hot strip mill process. Overall, the monitoring performance of the proposed method outperforms the traditional ones, in terms of higher fault detection rates and lower false alarm rates. Moreover, the information provided by the multi-subspace synergetic monitoring charts can offer valuable guidance to field engineers.