Dimensionality reduction (DR) plays a crucial role in various fields, including data engineering and visualization, by simplifying complex datasets while retaining essential information. However, achieving both high DR accuracy and strong explainability remains a fundamental challenge, especially for users dealing with high-dimensional data. Traditional DR methods often face a trade-off between precision and transparency, where optimizing for performance can lead to reduced explainability, and vice versa. This limitation is especially prominent in real-world applications such as image, tabular, and text data analysis, where both accuracy and explainability are critical. To address these challenges, this work introduces the MOE-based Explainable Deep Manifold Transformation (DMT-ME). The proposed approach combines hyperbolic embeddings, which effectively capture complex hierarchical structures, with Mixture of Experts (MOE) models, which dynamically allocate tasks based on input features. DMT-ME enhances DR accuracy by leveraging hyperbolic embeddings to represent the hierarchical nature of data, while also improving explainability by explicitly linking input data, embedding outcomes, and key features through the MOE structure. Extensive experiments demonstrate that DMT-ME consistently achieves superior performance in both DR accuracy and model explainability, making it a robust solution for complex data analysis. The code is available at https://github.com/zangzelin/code_dmtme