For example: I was hired by a company as a developer, and they loved me, I was very productive there. But just a few months into the employment, a competing company offered me a much higher salary with a much shorter commute. I went to my manager and told him all about the offer, and asked him what he would do in my shoes. He said he'd take the other offer (since he knew that a competitive counter-offer was impossible). I took the offer, and we parted on very good terms.
So you may be able to say something like this to this employee: "There seems to have been a misunderstanding about our expectations and your experience. We thought you had more experience relevant for this role. We don't want to leave you high and dry, but the current arrangement isn't tenable. Would you prefer to restart as a junior developer and work your way back up as you gain experience, or do you feel it would be better to part ways?"
Though now that I've typed it out, I'm not sure the strategy works as well when the one instigating the conversation has more power than the person being asked. Hmm. I'll post this in spite of my self doubt, just in case someone replies with interesting insights. I'm happy to be wrong if I learn something.