Within Teamwork.com, you can disable emails individually for each person so that they cannot be selected in the notification options.
Go to the People area of your project and select the People subsection.
Next to each project member's email address you will see an envelope icon. This will be green by default which indicates that they have email notifications are enabled for the project.
Click the envelope to disable email notifications. The envelope will display red when disabled.
You can click the envelope again to re-enable email notifications.
Note: The People tab in a project is accessible only to site administrators, project administrators, and users with permission to view people.
For more information, see: Project Notification Settings