Autonomous robotic assisted surgery (RAS) systems aim to reduce human errors and improve patient outcomes leveraging robotic accuracy and repeatability during surgical procedures. However, full automation of RAS in complex surgical environments is still not feasible and collaboration with the surgeon is required for safe and effective use. In this work, we utilize our Smart Tissue Autonomous Robot (STAR) to develop and evaluate a shared control strategy for the collaboration of the robot with a human operator in surgical scenarios. We consider 2D pattern cutting tasks with partial blood occlusion of the cutting pattern using a robotic electrocautery tool. For this surgical task and RAS system, we i) develop a confidence-based shared control strategy, ii) assess the pattern tracking performances of manual and autonomous controls and identify the confidence models for human and robot as well as a confidence-based control allocation function, and iii) experimentally evaluate the accuracy of our proposed shared control strategy. In our experiments on porcine fat samples, by combining the best elements of autonomous robot controller with complementary skills of a human operator, our proposed control strategy improved the cutting accuracy by 6.4%, while reducing the operator work time to 44 % compared to a pure manual control.