In this article, we propose an approach to extract variable-impedance during cutting tasks from human demonstrations, so as to ease soft-tissue cutting by robots. We model the dynamic adjustment of the human arm during interactions with the tissue and transfer these adaptive capabilities to the robot, by learning both the motion and change of impedance. To improve performance during task execution, our variable-impedance skill-transfer framework combines the learned model with an interactive-operation and feedback controller. To offer the flexibility of modifying the trajectory at run time, we use a control law based on dynamical systems. We couple this control law with virtual dynamics that describes the cutting dynamics. This ensures that the robot can control the interaction force and can plan the trajectory. The approach is validated in a real robot cutting-experiment of cutting different hardness tissues. Results show that our learning-based feedback controller, with the assistance from interactive-operation models, can effectively improve the task’s success rate, cutting length, cutting depth, and other indicators, as compared to using a fixed and variable-impedance gain controller.