Sepsis-induced acute respiratory failure (ARF) is a serious complication with a poor prognosis. This paper presents a deep representation learningbased phenotyping method to identify distinct groups of clinical trajectories of septic patients with ARF. For this retrospective study, we created a dataset from electronic medical records (EMR) consisting of data from sepsis patients admitted to medical intensive care units who required at least 24 hours of invasive mechanical ventilation at a quarternary care academic hospital in southeast USA for the years 2016-2021. A total of N=3349 patient encounters were included in this study. Clustering Representation Learning on Incomplete Time Series Data (CRLI) algorithm was applied to a parsimonious set of EMR variables in this data set. To validate the optimal number of clusters, the K-means algorithm was used in conjunction with dynamic time warping. Our model yielded four distinct patient phenotypes that were characterized as liver dysfunction/heterogeneous, hypercapnia, hypoxemia, and multiple organ dysfunction syndrome by a critical care expert. A Kaplan-Meier analysis to compare the 28-day mortality trends exhibited significant differences (p < 0.005) between the four phenotypes. The study demonstrates the utility of our deep representation learning-based approach in unraveling phenotypes that reflect the heterogeneity in sepsis-induced ARF in terms of different mortality outcomes and severity. These phenotypes might reveal important clinical insights into an effective prognosis and tailored treatment strategies.