Is it possible to separate/remove sugar from common drinks, such as juice?
Why not add yeast to your juice and allow it to ferment?  This will depend on the juice having pH and sugar concentrations; look at commercial wine making kits which provide the proper equipment and recipes. If you conduct the fermentation properly without introduction of air, the sugar will be converted to alcohol, which later can be boiled off (see above) to give the sugar-free version of your juice. Otherwise, with air present, the fermentation will go on to form acetic acid and give the juice a vinegary taste.