Weebly offers clear directions on how to unpublish a site. WordPress also provides options for users who want to restrict published content during a revision process or remove published content all together.
You can unpublish digital text using the tools listed above. That said, if Google or other search engines cache your site though, the unpublished content might be recovered. Which is to say, you should expect that something you or someone else publishes to the web will remain on the web.
That content once published online may remain indefinitely available to audiences is an argument in favor of managing your own domain. It is especially important that one of the first results when someone searches your name is a site that you control and that you can publish/unpublish to, shape, and control. If you have a strong domain presence, then having a section of your site that you uncover or unpublish might not actually eradicate all traces of it, but it will make it less prominent and someone would have to be really digging to find something you unpublish. Similarly, if you post something to Facebook, say, and then delete it, but you don't have a domain there's a decent chance that one way or another, that photo ends up resurfacing and potentially becoming the first thing someone sees when they search for you. Domain allows you to balance the advantages of publishing content for a community of users against potential harm.
John Udell argues along these lines in his "Disruptive Nature of Technology" podcast.