I don't think they thought to make actual buttons for that. I usually just hit ctrl-c/ctrl-v. I bet if you went to the opera forums they'd help you whip up a couple of custom buttons if you really want them.
I'm trying to get the features I use for I.E. to work w/ Opera. It was bothering me that Opera doesn't "remember" previous entries filled out in forms (don't know how to describe this properly), and in particular on Yahoo I would be able to hit the down arrow and it listed frequently used email addresses so I didn't have to look them up/type them in. I found out that you can insert fields from their Notes tool, so I added email addresses there and it works like a charm. But cut/copy/paste is the only one I couldn't figure out a substitute.