Within Teamwork Projects, you can choose not to receive emails when a member of your team updates their status.
To disable this, click on your profile icon in the top right corner of your site, and select 'Edit my Details':
You can now select the 'Preferences' tab of the light box that appears. You will then have the option to toggle on or off 'Receive status update emails?':
For more information see: Using team status updates