Lovely button! I think it is the Arms of Saxony, German State. Here is a listing for another described in the The Emilio Collection of Military Buttons at Google Books in the "Miscellaneous Non-Military" chapter.
Also I could only access with a Google cache view but here is another button similar "Sachsen" is Saxony in German.
Described as: A plate below shows eight different heraldic cuff buttons worn by military personnel from various German states attending Infantry Musketry School.
I don't know exactly how your button should be classified - just passing along what I found. It may be worthwhile to research the site history and see if you can find a connection.