Because this is a neighbor, I think you have to do this differently than you would if she weren't. You want to stay on civil terms, but not be friends. You want to be able to say hello and wave if you want to, but not hang out like friends do.
So I think you deflect deflect deflect. She calls you, or emails, or texts, you respond if you want to with quick, "Gosh, just so busy, don't have time to _____ right now." Every time. You don't let her in if she comes to the door, but you don't slam the door in her face either. You're cordial but not friendly. If she asks you about your "relationship" you say, "Gosh, I can't imagine what you're talking about," then beandip and then scurry off.
You don't have to give her the cut direct. It may take some time, and it will definitely take some patience on your part, but she will eventually get the message (I hope!).
This preserves neighborhood harmony, and it also let's you take the high road. You're not creating drama. You're just going about your business, and you're being nice about it.
That's how I think you should do it. It might not be as immediately gratifying as just cutting her off, but in the long run, I think you'll feel better about it.