The definition of supernatural is not circular, but it is not coherent either.
Questioner: What is supernatural?
Physicist: The word is defined as "above or beyond natural".
Q: You mean beyond scientific laws?
Physicist: Yes. "natural" is a word with a lot of meanings, but for me "natural" as opposed to "supernatural" means "allowed by the laws of the physical universe". However everything that happens obeys the laws of nature.
Q: Do you mean that science has a complete picture of reality? Your laws don't explain everything.
P: No, we can't explain eveything yet. There's the actual laws of nature, and then there's the approximations and parts that we know about. But we keep trying to make our picture more complete. The aim of physics and of all science is to observe reality in order to understand it. It's a process as much as it is a product.
Q: What if something "supernatural" or "impossible" were to happen? What if there was scientific evidence that it had happened? Would it be natural then?
P: Yes. If an event happens, it is by definition natural and possible. Impossible and "above the laws of physics" events do not happen, by definition. All that would have happened would be that our theories of what was impossible would have been proved incorrect. Reality behaves in predictable and understandable ways, it is not random or inexplicable. There is always a scientific way to describe all things that happen, even if we don't know it. Yet.
Q: But ESP is proven! So then ESP and other supernatural occurrences are scientific?
P: Extraordinary claims demand extraordinary proof and the proof for ESP just isn't there, despite a lot of trying. I think that ESP is just wishful thinking, but I'm willing to take a skeptical look at any evidence if I think it's worth my time. That's what science is all about.
Q: What about other supernatural interventions?
P: Some people like to believe that a "higher power" intervenes occasionally to cause events to happen that are not in accordance with the normally observed laws of physics, or do not have any natural cause. If we saw that, it would be natural by definition, and a theoretical framework could be built up to describe and predict such occurrences. The universe that is, is in principle understandable.
But such occurrences have not been systematically observed.
Q: But people have seen all kinds of things.
P: People claim, and even believe that they have seen all kinds of things. That's not the same as those things existing. Human perception and memory are highly fallible. We have high standards of proof. Independently verified, measurable evidence is required.
Q: So what is supernatural?
P: The idea of a "supernatural occurrence" is meaningless.
Another writeup-as-reply (to a writeup that has been deleted).
The physicist in my writeup does not speak with exactly my voice, but with a part of it. I wanted to give a more sensible answer than artfuldodger did, in line with the scientific worldview which I felt was being misused as a straw man.