Contagions (e.g. virus, gossip) spread over the nodes in propagation graphs. We can use the temporal and textual data of the nodes to compute the edge weights and then generate subgraphs with highly relevant nodes. This is beneficial to many applications. Yet, challenges abound. First, the propagation pattern between each pair of nodes may change by time. Second, not always the same contagion propagates. Hence, the state-of-the-art text mining approaches including topic-modeling cannot effectively compute the edge weights. Third, since the propagation is affected by time, the word-word co-occurrence patterns may differ in various temporal dimensions, that can decrease the effectiveness of word embedding approaches. We argue that multi-aspect temporal dimensions (hour, day, etc) should be considered to better calculate the correlation weights between the nodes. In this work, we devise a novel framework that on the one hand, integrates a neural network based time-aware word embedding component to construct the word vectors through multiple temporal facets, and on the other hand, uses a temporal generative model to compute the weights. Subsequently, we propose a Max-Heap Graph cutting algorithm to generate subgraphs. We validate our model through comprehensive experiments on real-world datasets. The results show that our model can retrieve the subgraphs more effective than other rivals and the temporal dynamics should be noticed both in word embedding and propagation processes.