First, make sure MailDrop is enabled. I don't own an iPad mini but this may help.
- Choose Mail > Preferences, click Accounts, select the account, click Advanced, then select or deselect “Send large attachments with Mail Drop.” (Steps may vary based on the iOS version.)
This link points out that only IMAP email accounts had a checkbox to activate the MailDrop/iCloud option.
One thing I noticed is it may not prompt MailDrop but it may still use MailDrop on the background if you made sure you enabled MailDrop for that account.
You can check that by sending a test email with large attachment and check the inbox of the recipient . If it shows a preview similar to the one below, it already used MailDrop.
Let me know if you have further questions, or if this doesn't solve your problem.