Brandcast saves all the changes you make to your website automatically, as you work. There's no need to manually save.
Note that this applies to your work in design studio, NOT to the published version of your site. The published website will only be updated when you click the "Publish Changes" button in the top toolbar.
If you need to undo changes that you've made in the studio, you can easily do so using the undo / redo function. There's a long undo history that you can view via the History Panel, which you can use to return to older states of your website.
Keep in mind that if you refresh your browser, or close the tab and open Brandcast in a different tab, you will lose your undo history.