I don't believe Mail has that sort of functionality built in--that is, it will always keep a sent message and the only way you could delete it would be to open the Sent folder. And my quick check indicates that for Outlook you can turn off the saving of Sent messages, but not limited to just one message.
The obvious solution is to filter the Sent folder automatically and specify criteria that will *ONLY* match the email you don't want to keep a copy of. Unfortunately as it comes out of the box Mail doesn't appear to allow you to set a rule to run automatically on the Sent folder.
However, I did find a reference to a Mail add-on that claims to do this--but a warning that I've not tested it and it's not free. The program is Mail Act-On and it's available at http://www.indev.ca/MailActOn.html. It costs $24.95, but it does claim to allow automatic rules to run on the Sent folder. There is a 30 day trial.
Realize that you need to be *very* careful when designing the rule to assure there are no unexpected consequences given the rule is going to delete the message. If you don't define the rule narrowly enough you could easily end up deleting far more than you expect to delete. So be *REAL* careful and check to be sure the only things deleted are the messages you want to be deleted.
Not automatic, but built in (meaning no additional cost) and safer would be to define a Smart Mailbox that looks at the Sent folder and then lists the offending messages. That should allow you to manually delete them, and has the advantage of allowing you to see if your condition is broader than you would like. If you clean out that Smart Folder every so often you'll get to the same point, but without the risk of something unexpectedly getting trapped in your filter and deleted without your knowledge.
Even if you want to use the automated process, I'd suggest a Smart Mailbox to get started. That will allow you to test out your filtering ideas to make sure the messages tagged are only the ones you really want to delete. Once you are absolutely sure you could duplicate the search in the add-on I mentioned above and let it delete the message. But be very aware of the risk of an automated delete.