Drop all the [non-essential objects][1], such as indexes,  from the DB (or a copy of it).

Some further ideas on Stack Overflow in the Q & A [Reducing Size Of SQL Backup?][2].

There are tools which will extract a referentially correct set of data from a DB. The one I used was for DB2, however. If I find a link for SQL Server I'll edit it in.

  [1]: https://www.brentozar.com/archive/2010/02/how-to-really-compress-your-sql-server-backups/
  [2]: https://stackoverflow.com/questions/1305107/reducing-size-of-sql-backup