Multivariate time series (MTS) have specific features that complicate their analysis: interactions in space and time between the MTS components, variable length, absence of trivial alignment between samples and high dimensionality. Hence, finding a representation of MTS from which we can extract meaningful information is a challenging task. In general, specific assumptions are needed to obtain a valuable representation. In this paper, we assume that a dataset of MTS samples has an underlying causal structure that we can exploit to represent samples. Our contribution is a new representation framework that consists of first finding the overall causality graph G in a studied dataset and then mapping each sample onto G to obtain a causality-based representation. Since causality is an important feature underlying MTS data, we claim and show that representating samples on G is meaningful. We name this method Sequence-to-Graph (Seq2Graph). We apply Seq2Graph on health monitoring tasks, using two MTS datasets coming from ageing mechanical systems.