In general, Neo4j Enterprise has a backup tool that backs up to fully operable graph database directories.
You could shutdown, zip it up and upload it.
Or just set up a Neo4j cluster that uses the remote servers as replicas.
If you want to have continuous updates, then that would be more involved (reading tx log and sending deltas or the same with triggers).
It's def. a valuable request, but usually a "live connection" would also send, e.g. deletes so your remote instance would be in sync with your local state, which might not what you need for a backup.
Michael