Just put the test-delete-db-extension-VERSION.jar for your Neo4j-VERSION into neo4j-server/plugins and add this to the server properties file
org.neo4j.server.thirdparty_jaxrs_classes=org.neo4j.server.extension.test.delete=/db/data/cleandb
org.neo4j.server.thirdparty.delete.key=secret-key
Then you can issue
curl -X DELETE http://localhost:7474/db/data/cleandb/secret-key
to delete the graph database without restarting the server