Skill propagation among robots without human involvement can be crucial in quickly spreading new physical skills to many robots. In this respect, it is a good alternative to pure reinforcement learning, which can be time-consuming, or learning from human demonstration, which requires human involvement. In the latter case, there may not be enough humans to quickly spread skills to many robots. However, propagation among robots without direct human supervision can result in robotic skills mutating from the original source. This can be beneficial when better skills might emerge or when a new skill is obtained to be used for other similar tasks. However, it can also be dangerous in terms of task execution safety. This letter studies the mutation of a robotic skill when it is propagated from one robot to another during a physically collaborative task. We chose the collaborative sawing task as a study case since it involves complex two-agent physical interaction/coordination and because its periodic nature can facilitate repetitive learning. The study employs periodic Dynamic Movement Primitives and Locally Weight Regression to encode and learn the motion and impedance required to execute the task. To explore what influences mutation, we varied several control and environment conditions such as the maximum stiffness, robot base position, friction coefficient of the sawed object, and movement period. The results showed that the skill varied over propagation steps and we identified several key aspects of mutation such as movement length, movement offset, and trajectory shape. Based on the results we identified possible benefits (skill mutations useful for different settings or different tasks, and energy efficiency) and dangers (high forces and skill mutations becoming useless for the original task) of the mutation.