Uhhhhh, yah that makes sense.
Wget is seeing your site like a web browser, so it doesn't automatically know where everything in your site's directory is located at.
Assuming your main index page only points to 6 other files, wget will only get those files and nothing more.
Adding --mirror won't do anything in this case.
What I would suggest, is either use wget and throw in an ftp link.. like: wget --mirror ftp://username@password:127.0.0.1:21/mysite.com
In this way it logs into your ftp server and grabs everything under the folder 'mysite.com'.
Either that, or you if you have SSH access on the other server, you just tar up everything and send it over to the other one.