UAV tracking can be widely applied in scenarios such as disaster rescue, environmental monitoring, and logistics transportation. However, existing UAV tracking methods predominantly emphasize speed and lack exploration in semantic awareness, which hinders the search region from extracting accurate localization information from the template. The limitation results in suboptimal performance under typical UAV tracking challenges such as camera motion, fast motion, and low resolution, etc. To address this issue, we propose a dynamic semantic aware correlation modeling tracking framework. The core of our framework is a Dynamic Semantic Relevance Generator, which, in combination with the correlation map from the Transformer, explore semantic relevance. The approach enhances the search region's ability to extract important information from the template, improving accuracy and robustness under the aforementioned challenges. Additionally, to enhance the tracking speed, we design a pruning method for the proposed framework. Therefore, we present multiple model variants that achieve trade-offs between speed and accuracy, enabling flexible deployment according to the available computational resources. Experimental results validate the effectiveness of our method, achieving competitive performance on multiple UAV tracking datasets. The code is available at https://github.com/zxyyxzz/DSATrack.