A pulling tool is used for setting or removing an internal component of a rotating control device (RCD). The pulling tool includes keys that extend outward for engaging with an inner surface of the internal component. The keys are spring loaded so that as the pulling tool is pressed through the internal component, the keys collapse inward until the keys are moved into a mating internal groove profile on the inner surface of the component. The pulling tool is able to selectively engage with and release from the component, both when the component is disposed in the RCD and when outside the RCD. This facilitates a mechanized installation and/or removal of the internal component from the RCD without relying on a friction force and without applying a torque or providing hydraulic fluid to the pulling tool.