Dimension reduction (DR) is commonly utilized to capture the intrinsic structure and transform high-dimensional data into low-dimensional space while retaining meaningful properties of the original data. It is used in various applications, such as image recognition, single-cell sequencing analysis, and biomarker discovery. However, contemporary parametric-free and parametric DR techniques suffer from several significant shortcomings, such as the inability to preserve global and local features and the poor generalisation performance. On the other hand, regarding explainability, it is crucial to comprehend the embedding process, especially the contribution of each part to the embedding process, while understanding how each feature affects the embedding results that identify critical components and help diagnose the embedding process. To address these problems, we have developed a deep neural network method called DMT-EV, which provides not only excellent performance in structural maintainability but also explainability to the DR therein. DMT-EV starts with data augmentation and a manifold-based loss function to improve embedding performance. The explanation is based on saliency maps and aims to examine the trained DMT-EV parameters and contributions of components during the embedding process. The proposed techniques are integrated with a visual interface to help the user to adjust DMT-EV to achieve better DR performance and explainability. The interactive visual interface makes it easier to illustrate the data features, compare different DR techniques, and investigate DR. An in-depth experimental comparison shows that DMT-EV consistently outperforms the state-of-the-art methods in both performance measures and explainability.