What I want to do, is have the Arduino ground that circuit and cut off the power to the LED. I'm only using the LED circuit as an example since if it works with those current hungry buggers then it should work with anything right?
Well there is probably a valid question in there somewhere ;), but the example is very poor in my opinion. An Arduino output pin can both actively sink (ground out) and source (provide +5vdc). The problem is there is a maximum current flow allowed from a output pin no matter if it's high or low of 40ma maximum (30ma recommended). So your example of having a output pin 'ground out' the board's +5 volt is generating a 'short circuit' condition and will surely damage the output pin.
So if you can actually supply a circuit drawing of what you are trying to do, there would be a better chance of getting proper advice if it is possible or not.
Lefty