This doesn't help you with the mouse, but if you just want to access the system clipboard this may help. If you type vim --version in the shell and one of the features is +xterm_clipboard then you should be able to access X's clipboard with the + register. The Arch wiki has a bit more information about this.
You can try compiling vim yourself to enable this feature with:
./configure --with-x --enable-gui=auto --with-features=huge
Or try installing the vim-gnome package which should have that feature enabled.
To use, preface relevant commands with "+ which instructs vim to use the + register. So to copy the current line to the clipboard: "+yy. To paste the contents of the clipboard: "+p.