Sepsis is a heterogeneous clinical syndrome that is the leading cause of mortality in hospital intensive care units (ICUs). Identification of sepsis subphenotypes may allow for more precise treatments and lead to more targeted clinical interventions. Recently, sepsis subtyping on electronic health records (EHRs) has attracted interest from healthcare researchers. However, most sepsis subtyping studies ignore the temporality of EHR data and suffer from missing values. In this paper, we propose a new sepsis subtyping framework to address the two issues. Our subtyping framework consists of a novel Time-Aware Multi-modal auto-Encoder (TAME) model which introduces time-aware attention mechanism and incorporates multi-modal inputs (e.g., demographics, diagnoses, medications, lab tests and vital signs) to impute missing values, a dynamic time wrapping (DTW) method to measure patients' temporal similarity based on the imputed EHR data, and a weighted k-means algorithm to cluster patients. Comprehensive experiments on real-world datasets show TAME outperforms the baselines on imputation accuracy. After analyzing TAME-imputed EHR data, we identify four novel subphenotypes of sepsis patients, paving the way for improved personalization of sepsis management.