Electronic healthcare records (EHRs) are comprehensive longitudinal collections of patient data that play a critical role in modeling the disease progression to facilitate clinical decision-making. Based on EHRs, in this work, we focus on sepsis -- a broad syndrome that can develop from nearly all types of infections (e.g., influenza, pneumonia). The symptoms of sepsis, such as elevated heart rate, fever, and shortness of breath, are vague and common to other illnesses, making the modeling of its progression extremely challenging. Motivated by the recent success of a novel subsequence clustering approach: Toeplitz Inverse Covariance-based Clustering (TICC), we model the sepsis progression as a subsequence partitioning problem and propose a Multi-series Time-aware TICC (MT-TICC), which incorporates multi-series nature and irregular time intervals of EHRs. The effectiveness of MT-TICC is first validated via a case study using a real-world hand gesture dataset with ground-truth labels. Then we further apply it for sepsis progression modeling using EHRs. The results suggest that MT-TICC can significantly outperform competitive baseline models, including the TICC. More importantly, it unveils interpretable patterns, which sheds some light on better understanding the sepsis progression.