You can turn off the Automatic Payment Notifications across your account by,
1. Clicking 'Account'
2. Select 'Settings'
3. Click on the 'Notifications' link located in the left side Account menu
4. Toggle 'Off' 'Send Payment Due Notification'
If you've disabled Payment Reminders on the account level, it will disable for all existing projects.
You can also disable Payment Due Reminders per project. Learn more here.