I'm going to cut off someone that considers me to be their best friend
Do you think this person deserves this?
No, but I don't like the attention they give me.
You can stop being a friend to someone at any time for any reason. If you don't like the attention they are giving you, you can stop talking to them at any point.
I'm going to let them know on their facebook wall. That Should get the point across.
Ending your friendship with them is fine but you shouldn't post it on their wall. It is a private matter between you two so you shouldn't post it for others to see. Instead, just send them a message if you don't want to talk to them face to face.