The files are still being copied across the network - effectively slowing down both both the MBLD and the USB drive attached to it - because in a network copy - all the data that you are copying is being transferred via SMB or AFP from the external USB drive - through the MBLD's network interface - through your laptop - and back through the MBLD's ethernet port into the USB drive. All of this is relatively slow. You can speed this up by connecting your laptop to your network with an ethernet cable - assuming that your network has a gigabit infrastructure - however - if it is a 100 megabit wired network - you will see some improvement but not that much. This is not a a problem with the MBLD - rather it is a limitation with network file transfers in general.
I am not familiar with the MBLD - but if there is by any chance a file copy utility built into the MBL firmware - you would log into the MBLD's dashboard and initiate the copy from there - and that would have the best chance of approaching the MBLD's full drive speed as well as maximizing the transfer to the USB drive. If this functionality does exist - you would find it in the MBLD's dashboard.
Another thing you could try - if you have enough space on your laptop - would be to connect your laptop to your wired network - copy the files from the MBLD's internal drive to your laptop - and then copy them from your laptop to the USB drive attached to the MBLD. This should be faster than network copying from the MBLD to the USB drive.
A third option would be to attach the USB drive to a USB port on your laptop - and then attach the MBLD to your laptop by plugging the MBLD's ethernet cable directly into the ethernet port of your laptop. This will cause the MBLD to assign itself a 169.254.x.x self-assigned ip. You will be bypassing your LAN and you should be able to greatly improve the transfer spped over and above what you were getting on your LAN - at least in the scenario you have described. If this copying is a one-time event (or an infrequent event) then it is feasible to do this - but if it is a regular event - then it could prove to be somewhat painful.
Be sure to completely shutdown your MBLD via the dashboard before disconnecting from the network and connecting directly to your laptop.