I'm a little confused... are you referring to saving a "post" as a draft? If you save a post as a draft, you wouldn't publish it so it would not be visible on the web site, so I'm not sure I follow when you say that "it removes the previous version from the web". Am I completely misunderstanding what you've said?

When using Wordpress as a webpage it's different than using Wordpress as a blog. What I'm asking about is when it is used as a website and you are working on a page (not post) and try to save it as a draft.

Ah, a page, not a post. I hadn't noticed this because I keep new pages set to private while drafting them and once they are live, the changes are minimal enough that it is not a problem that my working copy is my live copy.

When you are going to make substantial edits to a page that you would want to be able to keep in draft format without any changes being made to the live page, could you start a new page (set to private) and cut/paste from your existing page to the new page to use as a working copy and then when it is ready to publish cut/paste from the working page to the live page? There may be a few things that don't work right on your working page because of naming, etc. but it should work good enough to be an effective working copy. Most of the stuff on the page itself is just content as the vast majority of formatting/coding is in the page template, the sidebar templates, and the stylesheet.