not really sure what the end-game is here but this is how to do a standard file copy of all files in a subdirectory:
cp -r /path/to/source /path/to/destination
is what tells cp
ecurse into sub-directories (obviousely you have to change the source
specific to your needs).
edit: maybe this should be done while using something like gparted-live-usb so that you can make an image copy of the usb partition rather than file-by-file copy.
else it mite work if you make your source directory /
and the destination somewhere under your internal hd mount-point (but there will be random /proc
files that only make sense to a running system).