Within Teamwork.com, you can choose not to receive emails when members of your site update their status.
Click your profile avatar in the bottom left of your site and select Edit my details from the pop-out menu.
Go to the Preferences tab of the user details modal. You can then toggle on or off the option to Receive status update emails.
Click Update to save your changes to your notification preferences.
For more information, see: Using Team Status Updates