The objective of this study is to propose MD-VAE: a multi-task disentangled variational autoencoders (VAE) for exploring characteristics of latent representations (LR) and exploiting LR for diverse tasks including glucose forecasting, event detection, and temporal clustering. We applied MD-VAE to one virtual continuous glucose monitoring (CGM) data from an FDA-approved Type 1 Diabetes Mellitus simulator (T1DMS) and one publicly available CGM data of real patients for glucose dynamics of Type 1 Diabetes Mellitus. LR captured meaningful information to be exploited for diverse tasks, and was able to differentiate characteristics of sequences with clinical parameters. LR and generative models have received relatively little attention for analyzing CGM data so far. However, as proposed in our study, VAE has the potential to integrate not only current but also future information on glucose dynamics and unexpected events including interactions of devices in the data-driven manner. We expect that our model can provide complementary views on the analysis of CGM data.