An ever-growing incorporation of AI solutions into clinical practices enhances the efficiency and effectiveness of healthcare services. This paper focuses on guidewire tip tracking tasks during image-guided therapy for cardiovascular diseases, aiding physicians in improving diagnostic and therapeutic quality. A novel tracking framework based on a Siamese network with dual attention mechanisms combines self- and cross-attention strategies for robust guidewire tip tracking. This design handles visual ambiguities, tissue deformations, and imaging artifacts through enhanced spatial-temporal feature learning. Validation occurred on 3 randomly selected clinical digital subtraction angiography (DSA) sequences from a dataset of 15 sequences, covering multiple interventional scenarios. The results indicate a mean localization error of 0.421 $\pm$ 0.138 mm, with a maximum error of 1.736 mm, and a mean Intersection over Union (IoU) of 0.782. The framework maintains an average processing speed of 57.2 frames per second, meeting the temporal demands of endovascular imaging. Further validations with robotic platforms for automating diagnostics and therapies in clinical routines yielded tracking errors of 0.708 $\pm$ 0.695 mm and 0.148 $\pm$ 0.057 mm in two distinct experimental scenarios.