How do I automate adding opt-outs to a global list?

Using the API you could write a custom interface to your proprietary system. That interface would then run on some set schedule. Without the API, you would have to export your contact list manually and select the option to only include those who opted-out. Then you need to bring that list into your system to update their status.

@DebH_AUS, Are you using Directory IQ or Research Core contacts?

Hi Tom. We're using Directory IQ. thanks

@DebH_AUS, We've done it this way... Create an opt-out survey with embedded data for email and respondent id and a single text entry question that asks for email pre-populated with the email embedded variable. From the survey flow call a web service script that uses the Qualtrics API to opt them out of Qualtrics and sends the information to your proprietary systems. You can screen out all responses so they don't count against your Qualtrics quota. In your email invite hide the Qualtrics opt-out and add an opt-out link that points to your opt-out survey with piped-in parameters for email and respondent id.

Hi, I need to do the same but with a Research Core API. Is it possible?

Yes, but Research Core opt-outs only apply to a single list. So, if you need a global opt-out list, you need to store it externally to Qualtrics.