Cutting everyday food items presents a significant challenge in robotics due to the multiple types of knife skills and the unpredictable mechanical behaviour of materials during manipulation. To address this, we propose a one-shot demonstration-based framework that integrates the imitation of both position and force trajectories of knife skills using dynamic movement primitives (DMPs). Our approach combines: (1) a compensation method to replicate human-like force trajectory, and (2) skill-specific constraints enabling online trajectory re-planning during cutting. We designed three knife skill demos for the robot and tested them on 14 unknown food items. The experiments are conducted to evaluate the effectiveness of the proposed force compensation and re-planning methods. The results demonstrate that our framework can successfully imitate various knife skills and cut previously unknown food items with high precision.