mavericks mail breaking sent folder
Assuming I understand your question correctly:

It all starts with in the origin.

In your case it is the Gmail.

First go to Gmail and settings and disable the "show in IMAP" for Send messages.

It looks like this:



Now Gmail will not longer send you the send messages.

However, next you need to do is also to tell the Mail.app not to save the Send mails on Server.

That is done here