Breast cancer is the leading cause of cancer-related deaths among women worldwide, and early detection and treatment has been shown to significantly reduce fatality rates from severe illness. Moreover, determination of the human epidermal growth factor receptor-2 (HER2) gene amplification by Fluorescence in situ hybridization (FISH) and Dual in situ hybridization (DISH) is critical for the selection of appropriate breast cancer patients for HER2-targeted therapy. However, visual examination of microscopy is time-consuming, subjective and poorly reproducible due to high inter-observer variability among pathologists and cytopathologists. The lack of consistency in identifying carcinoma-like nuclei has led to divergences in the calculation of sensitivity and specificity. This manuscript introduces a highly efficient deep learning method with low computing cost. The experimental results demonstrate that the proposed framework achieves high precision and recall on three essential clinical applications, including breast cancer diagnosis and human epidermal receptor factor 2 (HER2) amplification detection on FISH and DISH slides for HER2 target therapy. Furthermore, the proposed method outperforms the majority of the benchmark methods in terms of IoU by a significant margin (p<0.001) on three essential clinical applications. Importantly, run time analysis shows that the proposed method obtains excellent segmentation results with notably reduced time for Artificial intelligence (AI) training (16.93%), AI inference (17.25%) and memory usage (18.52%), making the proposed framework feasible for practical clinical usage.