You need to stop code that is continuously processing. If you have a Timer running that controls activity, then you need to stop the Timer. If you have an ENTER_FRAME event listener active, you need to deactivate it... and so on with anything else that is running by itself.
Another option would be to build conditional code into the event handler functions that only allows the functions to process based on a boolean value... such as you create a boolean variable named "gamePaused" and then in your code where you need to have automatic activity occuring you use it as a precodnition...
// process activity