Recent studies have shown that deep learning-based hyperspectral image (HSI) classification models are highly vulnerable to adversarial attacks, posing significant security risks. Although most approaches attempt to enhance robustness by optimizing network architectures, these methods often rely on customized designs with limited scalability and struggle to defend against strong attacks. To address this issue, we introduce adversarial training (AT), one of the most effective defense strategies, into the hyperspectral domain. However, unlike conventional RGB image classification, directly applying AT to HSI classification introduces unique challenges due to the high-dimensional spectral signatures and strong inter-band correlations of hyperspectral data, where discriminative information relies on subtle spectral semantics and spectral-spatial consistency that are highly sensitive to adversarial perturbations. Through extensive empirical analyses, we observe that adversarial perturbations and the non-smooth nature of adversarial examples can distort or even eliminate important spectral semantic information. To mitigate this issue, we propose two hyperspectral-specific AT methods, termed AT-HARL and AT-RA. Specifically, AT-HARL exploits spectral characteristic differences and class distribution ratios to design a novel loss function that alleviates semantic distortion caused by adversarial perturbations. Meanwhile, AT-RA introduces spectral data augmentation to enhance spectral diversity while preserving spatial smoothness. Experiments on four benchmark HSI datasets demonstrate that the proposed methods achieve competitive performance compared with state-of-the-art approaches under adversarial attacks.