Precisely reconstructing and manipulating crumpled cloths is challenging due to the high dimensionality of the cloth model, as well as the limited observation at self-occluded regions. We leverage the recent progress in the field of singleview human body reconstruction to template-based reconstruct the crumpled cloths from their top-view depth observations only, with our proposed sim-real registration protocols. In contrast to previous implicit cloth representations, our reconstruction mesh explicitly indicates the positions and visibilities of the entire cloth mesh vertices, enabling more efficient dual-arm and single-arm target-oriented manipulations. Experiments demonstrate that our template-based reconstruction and targetoriented manipulation (TRTM) system can be applied to daily cloths with similar topologies as our template mesh, but have different shapes, sizes, patterns, and physical properties. Videos, datasets, pre-trained models, and code can be downloaded from our project website: https://wenbwa.github.io/TRTM/.