Discourse will automatically save a single “new topic” draft (after the ‘saved’ message appears when you pause typing). This does save on the server and allows you to return to your new topic on another device.
I think the Discourse team are deliberately trying to avoid a complex topic draft feature, so if you need a more robust method of saving a post, you will need to save it externally. I recommend using gist.github.com, as your Gists are associated with your GitHub account. Also, if you name the Gist as <filename>.md, it will automatically be rendered as a Markdown file, which will display formatting the same way it will display on Discourse whenever you do make your post.