There is no
copy command among the list of basic FTP commands. You have
get (pull a file from remote to local) and
put (push a file from local to remote) and that's it. If you want to make a copy of something on an FTP server you first have to download it and then upload it to the new location.
There might be FTP servers with extended command sets, but detecting this and writing the necessary special cases for these servers in to Transmit is likely more time consuming than it's worth.
I don't know of any graphical, remote file access tool that will do what you're asking for: execute the copy completely on the remote host instead of copying them down and then pushing them back up. It's really very rare that a remote file access protocol has a copy command like that.
For at-remote copying like that it's best to use a shell. As Gerry mentioned: ssh is the way to go here. With a remote shell, copy commands can be executed and run completely in the remote environment. Saving you bandwidth and potentially a lot of time.
If you'd like to see if your remote FTP server has an extended set of commands, try connecting to it using the command line ftp program:
> ftp user@hostname
And then running:
At the FTP prompt to see a list of commands the remote server supports. It may support an extended set of commands with
copy being one among them.