I don't believe there is anyway to do this in Gmail. When an email is sent it appears in the "Sent Mail" folder (or rather is assigned the
sent label) and there does not appear to be anyway to change this behaviour. "Filters" only act on incoming email.
However, you can do this in some other email clients, by essentially not saving the sent email:
You can set it to simply not use the "Sent" folder. Under Options > Folder Preferences > Special Folder Options > Set "Sent Folder" to "[Do not use Sent]":
In roundcube you can set this at the time you compose the email, by selecting "- don't save -" from the "Save sent message in" dropdown:
To make this the default option you can set this in Settings > Preferences > Special Folders and set the "Sent" folder to "---":
Mozilla Thunderbird (desktop email client)
In Thunderbird you can simply uncheck the "Place a copy in" checkbox, with regards to "sending messages" (in the appropriate account settings), and the sent email does not appear to be saved anywhere. The default behaviour is to save the sent email in the Sent folder on the email account.
In Account Settings > Copies & Folders > When sending messages, automatically: > Uncheck "Place a copy in".