I do this all the time, and the thing I still forget to do sometimes is to publish the page first, because that's when you can get to the attachments on a copied page.
After you publish, you should see the paper clip icon (at least that's what it looks like to me) at the top of the page, located to the right side of the breadcrumb. When you click the icon, it opens the Attachments page which is where you can delete attachments.
@Vickie Edwards On the Confluence page if you see all the way to the top right corner you will see three dots when you click on that option you would have see Attachments that are present in the current page.
You can click on that option and deleted the attachments present in the page and remember you would need the delete attachment permissions in the space before you can delete them from the page.
Hope this helps!