The alpha build of Elite: Dangerous doesn't appear to have a button to clear a control binding, or any indication of how to clear a control binding.
In my particular instance, I was playing with a mouse so was using the "Mouse and Keyboard" profile, which has bound my mouse to ship movements, but now I am playing with a gamepad and want to clear the mouse controls without changing my profile (since I've bound a variety of other controls since, and have already bound my gamepad).
How can I clear a control binding that has been set and reset it to nothing?