Hyperspectral image super-resolution (HSI-SR) aims to reconstruct high-resolution (HR) images from their low-resolution (LR) counterparts while preserving spectral integrity. Existing knowledge distillation (KD) methods predominantly transfer knowledge from a single super-resolution network, which limits the student model's ability to learn multi-stage hierarchical features. To overcome this limitation, we propose an asymmetric dual-teacher KD framework where two specialized teachers guide the student network: The super-resolution teacher network provides the knowledge of feature extraction, and the reconstruction teacher network provides the knowledge of feature reconstruction. Furthermore, we designed a Dual Aggregation Transformer U-net (DATU-Net) that is applicable to this framework and to hyperspectral super-resolution. The loss function designed enables the student network to focus on the knowledge of the two teacher networks, we verified the proposed network on two datasets and proved that our knowledge distillation framework is superior to the latest methods. The effectiveness of this framework was proved through ablation experiments.