When using a terminal like Putty, usually mouse clicks and selections are not transmitted to the remote system. So, vi has no idea that you just selected some text. (There are exceptions to this, but in general mouse actions aren't transmitted.)
To delete multiple lines in vi, use something like 5dd
to delete 5 lines.
If you're not using Vim, I would strongly recommend doing so. You can use visual selection, where you press V to start a visual block, move the cursor to the other end, and press d to delete (or any other editing command, such as y to copy).