First of all, as William P. Botha said there is absolutely no reason to use putty on Linux. Just open your favorite terminal emulator and run
ssh or whatever it is you need to do:
$ ssh firstname.lastname@example.org
$ scp local_file.txt email@example.com:/path/to/remote/file.txt
As for the clipboard, this gets slightly complicated under *nix. You are probably running afoul of the multiple clipboards offered by X (this is a feature, not a bug). Briefly, there are two main "clipboards" for *nix, the PRIMARY and CLIPBOARD. When you select text, that gets copied to the PRIMARY and can be pasted using the middle button of your mouse. Ctrl+C copies to the CLIPBOARD and can be pasted using Ctrl+V. So, depending on which clipboard is in use, you can paste using a different method. See this page on the Arch wiki for some more info.
You may also find one of the may "clipboard managers" useful. They allow you to switch between the clipboards in use and to save some previous selections in a sort of clipboard history to paste on demand. Some of the better known ones are: