Send your email to the first group, and then click on the 'View Recipients' button. At the bottom of the page, you will find the list of email addresses you sent your email to. Copy the list in your clipboard.

Manage the other group, click on 'Manage my members', and 'Members by tags' on the left, then click on "Tag builder". Enter a Tag Name (ex: "overlap"), paste your list of emails in the text area then click on Tag Emails.

Click on 'Compose an email' and once you have selected the group and clicked "Compose email for selected groups", you will see the list of recipients and their tags. The ones whom you have already emailed will be tagged with "Overlap" and you will need to uncheck the checkbox for them.