I assume you expected to have the text copied to the clipboard of the host system. I doubt that's possible from within vim running in a putty session but the following works for me
- select the text using the mouse.
- selected text is be put in my system's clipboard.
Note that this has nothing to do with vim but is entirely putty's doing.
Edit
From Using PuTTY
3.1.3.5 Copy All to Clipboard
This system menu option provides a convenient way to copy the whole
contents of the terminal screen (up to the last nonempty line) and
scrollback to the clipboard in one go
