If you want to completely turn off the auto tweet option
This can easily be done from the Twitter side by going to Settings > Applications and revoking our authorization -
Once you've revoked access at Twitter, it doesn't matter if you have "auto-tweet" turned on - our call will simply fail and nothing will show on Twitter.
If you just want to tweet selectively:
Don't forget, you have the option on each campaign to tweet upon sending or not tweet on the Setup step of the Campaign Builder. Just check or uncheck the send to Twitter option.
If you are replicating a campaign, the option is copied over to the new campaign like other campaigns options. You'll just need to uncheck the option it before sending.
If you've already sent the campaign, you can try to revoke access as noted above quickly to stop it. If it's scheduled or a Draft, you can pause it and remove the option to tweet on send on the Setup step.