How to remove Archive Category: X From DropDown Categories

Actually, much of what appears on the Archive page can be styled using Graphene’s custom CSS feature or a child theme. There is no need to hack into the theme’s core files. (Such hacks will be overridden at the next update.)

Try this tutorial for a way to alter archive pages via CSS:

http://blog.kjodle.net/2012/02/24/styling-wordpress-posts-pages-archives-and-home-pages-by-class/

Do you mean the actual text “Category Archive: For Whatever Category”?

If you want to hide that text, you can add this to custom CSS:

.archive h1.page-title {display:none;}

If you want to change the text to say something else, you will need a custom function. There are instructions for that on the Graphene forum:
http://forum.khairul-syahir.com/