In the IOS Mail app, you can override the Sent Mailbox settings (start at Account -> Advanced). As I recall, you cannot suppress saving a copy automatically, but can (for instance) send the copy to Trash or the desired IMAP folder.
I looked briefly at MailMate some time ago, but do not recall its handling of Mailbox preferences. Something in the back of my mind says that one of the reasons I did not evaluate it further was that it is inflexible in Mailbox management. Perhaps, someone else can help you with this.
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