The process of recycling electric vehicle (EV) batteries currently represents a significant challenge to the waste management automation industry. One example of it is the necessity of removing and sorting dismantled components from EV battery pack. This paper proposes a novel framework to semi-automate the process of removing and sorting different objects from an EV battery pack using a mobile manipulator. The work exploits the Behaviour Trees model for cognitive task execution and monitoring, which links different robot capabilities such as navigation, object tracking and motion planning in a modular fashion. The framework was tested in simulation, in both static and dynamic environments, and it was evaluated based on task time and the number of objects that the robot successfully placed in the respective containers. Results suggested that the robot’s success rate in accomplishing the task of sorting the battery components was 95% and 82% in static and dynamic environments, respectively.