This feature requires Author user level or higher.
Remove MailChimp authorization inside your Twitter account to turn off Auto-tweets. Even if a campaign is set to Auto-tweet, the connection will fail after permission is revoked.
To turn off Auto-tweet for a single campaign, navigate to the Setup step of the Campaign Builder, and check or uncheck the box for Auto-tweet campaign as.
When you replicate a campaign that has Auto-tweet turned on, that setting will be carried over to the replicated campaign. Uncheck Auto-tweet campaign as before sending.
Once a campaign is sent, you can revoke access as noted above to try to stop it from posting on Twitter. If the campaign hasn't been sent yet, you can remove the option to Auto-tweet on the Setup step.