Well, in mysql you have luxury of databases and tables. So you can dump all tables from one db, a list of named tables, or a list of named tables with a where expression applied.
But in neo there is just one "space" for data that is all connected and no much regarding types of nodes (unless some thing like Spring Data gives you that via _type_ field).
Here's a half-baked proposal for automatic subgraph extraction – just to keep conversation going.
Please take this with a grain of salt – I'm very new to the graph land still.
Half-Baked Proposal
I think the way to do this in graphs would be to specify some starting nodes and allowed traversal rules, and then export everything reachable from these starting points. All relationships affecting the selected nodes would also be included. Relationships between the nodes in the exported set are part of the subgraph, so they should be exported. Relationships that connect exported nodes with the rest of the graph should also be exported because they necessary to "reconnect" the subgraph to the destination graph upon import. This of course assumes some kind of unique key-based lookup of the nodes in the destination graph to reconnect with. And what if they are not found? Perhaps these relationships are then to be dropped or placeholder nodes created automatically?
In mysql land, equivalent of these relationships are foreign keys, which are defined at the table-to-table level (i.e. Node-type to node-type) and so they are already "present" in the destination db. All that's needed is to insert the rows and "relationships" are automatically re-established.