In addition, Steve is quite the right answer, you can also connect using psqlto DATABASE_URLand used \copy, for example.
$ psql "$(heroku config:get DATABASE_URL)"
mydb=> \copy mytable TO 'mytable.csv' WITH (FORMAT CSV, HEADER)
mydb=> \copy (SELECT col1, col2 FROM mytable2 WHERE ...) TO 'mytable2_partial.csv' WITH (FORMAT CSV, HEADER)
( ..). (DDL) , pg_dump --schema-only -t ....