CSS editing is theme specific. If you have custom CSS and later change themes, you need to delete whatever CSS you have in the Editor, otherwise, you’ll get undesired results.
To ‘reset’ a theme, you need to delete the CSS in the Editor, make sure the “add to existing CSS” radio button is checked, then save. Things should go back to normal.
I would like to know how could I work on my site to change it to the Mystique theme without altering its LIVE appearance.
As you have already done CSS editing you do know their is a preview function that you can use so visitors do not see your editing. Aside from that preview mode , there is no other way, other than changing the blog visibility setting to "private" to have one theme displaying while you work on editing CSS for another theme.