Q: Transferring 10  GB over the internet?

You need to find the public IP of the remote mini.

Are you able to use remote desktop (via back to my mac) on the mini ?

If so open the Terminal ant type the following command: curl http://automation.whatismyip.com/n09230945.asp

You will get the public IP of your router.

I recommend to use dynamic DNS service i.e. DynDNS (dyn.com) or NoIP (www.no-ip.com)

OK. Let's do it step by step.

Are you able to ssh to the mini ?

Open Terminal and type: ssh your_username_on_mini@external_ip_of_mini

If it fails it means that there is no port forwarding set up on your router, and it has to be done.

If you have spaces in your username use: "User Name"@external_address

In order to be able to access your mini via (CyberDuck SFTP) you need to set up port forwarding of your router.

It is not very complicated and needs to be done just once and will serve you well "forever".

Do you have configuration access to your roter ?

What kind of router is it: Linksys, D-Link ... ?

Yes.

What router / model do you use ?

1. Click Remove in the last row.

Add new definition.

1. Application name SSH

2. Protocol TCP

3. From 22

3. To: 22

4. Map to host port: 22

Assuming host is a mini internal IP (192.168.254.107) and you use default port 22 for SSH.

So now you should be able to use Transmit or Cyberduck with no problems.

For this solution to be stable over time make sure your mini's internal IP is static.

Is your mini's (router) external_IP static ? If so you can use the IP in the future.

If it is dynamic (your ISP changes it over time) I recommend to use DynDNS so you will be able to access your external _IP by name (the dyndns will reflect all the changes done to IP)