If you have a head set and it is not turned on (wireless) /plugged in (Wired) then the mick is off
If you have a Kinect. and it is plugged in, Then pressing the guide button (the big button on the controller) and scrolling Right 2 times and clicking Preferences and then voice. theres a check box that allows you to mute the kinect mic so no one can hear
If you are trying to stop all communications from your console you can use account safety settings by doing the following:
On Xbox home, scroll all the way right to system and click privacy. From there you can change a bunch of settings from comunications to online status
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