Just to be sure I've understood: you are copying music from the PC to the phone via USB. The reason you've only been able to move 2GB is presumably that you are running out of space? And the data are going to the phone's internal storage (not a hard drive) rather than the removable SD card?
So when you attach the device what drive(s) do you see? It sounds like it might only be mounting the internal storage, but I've not tried android 4.4 with SD strorage plus Linux Mint, so don't have direct experience of this combination.
One thing that's confusing if you are new is that if you look at the phone storage using a file browser on the phone you'll find an area called "/sdcard" which is actually part of the internal storage (the removable card may be called /sdcard1 or some variant of /extSdCard, depending on the manufacturer). This is basically for legacy compatibility with apps that assume "sd card" storage and devices that may not have an SD card in them, but irritating to purists like me
If my guess at what's happening here is correct your options are either to find a way of mounting the real SD card over USB - if the phone gives you that option (try going into the storage menu or pulling down the notifications while USB is connected) - or putting the card in a card reader and copying directly.
Unfortunately due to an over-zealous implementation of file security in 4.4 you may not be able to move the files that are already on the device to SD using a file browser without rooting the phone (it's better in 5!). If the phone comes with a built-in file manager that should be able to do it, as that will be installed as a system app, but it probably won't let you move them using a file manager you install yourself.