Meditrina -have you ever updated your iPhone software?
Cut and paste wasn't originally possible on the iphone3, but it came in with the 3.0 software version in the summer of 2009.
You can find out which version you have by going to Settings-General-About & looking under Version.
If you haven't got version 3.0 or higher, you won't be able to cut and paste, if you have, you should be able to.
I'm not sure if you could now update to 3.0, you might have to go straight to 4.2, which is the latest version & which I would be wary of putting on an iPhone 3G - I haven't risked it on my old one which DD now has though it seems to be OK on the 3GS.