You can right click on the table header, select Update sync configuration, click the three little dots beside the active source and remove it. When you click remove it will pop up a confirmation dialogue that confirms that the data will remain but will no longer be sync'd.

This appears to no longer be true:

It now says the records will be removed.

It is still true. You are probably seeing that because you are trying to unsync one of multiple sources.

I don't know a way of unsyncing a multi-source table without losing data (by doing a CSV export, for example.) If anyone has any tips about that, I'd love to hear them.

Hi Sean! I encountered this exact issue, and the workaround I found here was to convert the multi-source sync to a normal sync by: 

1) Syncing that multi-source table to another staging base

2) Syncing that new single source table back to my original base. (This was the easiest way to keep the field types the same and not have to readjust field types after a CSV export) 

Hope that helps!

I'm definitely going to try that, thanks for the idea!