How can i block someone from my facebook business page

Log in to Facebook from a computer, then switch to your Page. From your Page, click Manage, then click Page Access. Next to the person you want to remove, click then click Remove From Page.

They will not be able to like or comment on any of your pages posts and they won't be able to message your page directly. So it doesn't delete you from all existence on Facebook, but it does add a barrier for them interacting with you in that way. But you can ban and unbanned someone at any given time.