Copy-paste for vim is not working when mouse (:set mouse=a) is on?

I was trying to copy paste something from vim to another application and also, from that application to vim using right click with mouse and then copy and paste (or with Ctrl+v and Ctrl+c and also tried the Command version for mac OSX, obviously.). However, when I try doing it, it only copies the first word when I do it from vim or when I copy from the application to vim, it copies everything, but inserts strange tabs and spaces. I think this happened when I decided to set my mouse on in the terminal. As in: :set mouse=a I have that line on my .vimrc file on iTerm (mac os x). Though, is it possible to make my copy paste with other applications that are not in vim not to break with the mouse=a on? Or is it at least possible to set my mouse off while I do the copy paste? I did :help mouse but the comments were not useful for me. I would paste them here but... my copy paste tool is broken! I did try :set mouse! and :set mouse=a! but these did nothing useful... :( ---- Additional info of my environment: I am also using tmux most of the time, though, I tested this error/bug without a tmux session, thats why I posted this mainly as a vim question.