Sorry, I'm not a heavy user of the new Mail App, but in my testing I discover that
When I actually double click the email message in my inbox that has an attachment to open the actual email rather than view in in preview pane and then right click the attachment included in the email I get these two options
as depicted in the image below. I do not see or get an option to download.
View attachment 1546
Have you checked the Store App to see if you have any App updates pending
They should automatically download but it might be worth investigating.