Liver cancer is a leading cause of mortality worldwide, and accurate Computed Tomography (CT)-based tumor segmentation is essential for diagnosis and treatment. Manual delineation is time-intensive, prone to variability, and highlights the need for reliable automation. While deep learning has shown promise for automated liver segmentation, precise liver tumor segmentation remains challenging due to the heterogeneous nature of tumors, imprecise tumor margins, and limited labeled data. We present SmoothSegNet, a novel deep learning framework that addresses these challenges with the three key designs: (1) A novel knowledge-informed label smoothing technique that distills knowledge from clinical data to generate smooth labels, which are used to regularize model training, reducing the overfitting risk and enhancing model performance; (2) A global and local segmentation framework that breaks down the main task into two simpler sub-tasks, allowing optimized preprocessing and training for each; and (3) Pre- and post-processing pipelines customized to the challenges of each subtask aimed to enhance tumor visibility and refines tumor boundaries. We apply the proposed model on a challenging HCC-TACE-Seg dataset and show that SmoothSegNet outperformed various benchmarks in segmentation performance, particularly at smaller tumors (<10cm). Our ablation studies show that the three design components complementarily contribute to the model improved performance. Code for the proposed method are available at https://github.com/lingchm/medassist-liver-cancer.