While this probably can be done, we would need more information to be able to write it. Minimum that I can think of, would be the ftp site address.
Since the ftp site requires a login, then it would be almost impossible to correctly test any code written, unless the person that wrote it had an account for that site. (while not impossible, I wouldn't want to bet on it).
Also, for the file transfer, you're not going to manage to get FTP speeds using mIRC.
Personally, I think you'd be just as well, if not better, off getting an FTP program and using it. Some FTP programs will allow you to delete files from the remote location, presuming you have sufficient access to the remote location.
For FTP, I use FlashFXP