Egocentric action recognition aims to accurately model hand-object interactions. However, existing methods are highly susceptible to background noise and face challenges in balancing long-range and local feature modeling, alongside the high computational costs associated with processing high-resolution image sequences. To address these limitations, we propose a Taylor-Augmented Transformer-Mamba hybrid architecture(TATM). We first introduce Taylor Augmentation, a novel method based on Taylor frames, which employs a dynamic modality replacement strategy to generate a diverse training sample distribution, thereby enhancing model robustness against background interference. Additionally, we incorporate predicted object categories and decoded hand poses as part of the action recognition input, and design a MambaAction block adapted to Taylor-augmented data, which is integrated into the Transformer encoder. This hybrid framework enhances the modeling of hand-object interactions and effectively mitigates the trade-off between long-range dependency modeling and computational efficiency. Extensive experiments demonstrate that our approach doubles the inference speed for high-resolution images and achieves significant performance improvements on two skeleton-based egocentric action recognition benchmarks, FPHA and H2O.