How do I remove drafts from the iOS Notification Center?
Apple does hide the settings for the drafts folder pretty well, but in general you have a choice of saving drafts on the device or on your mail server.  It seems you have set them to be on the device.  I suggest moving them to the server. 

Here's how I get to the setting for my account.  Your path might be slightly different as I think it is different for different kinds of servers:


Settings
Mail, Contacts, Calendars
Under "Accounts", click on the mail account to bring up a popup with settings for that account
Select "Account" again
Select "Advanced"
Under "Mailbox Behaviors" select "Drafts Mailbox"
Under "On the Server" select the "Drafts" mailbox


I like having them on the server as then they are synced everywhere.