Schedule replication of SQL Server views to MySQL remote database
You'll want to look at SQL Server Replication.  If you just want a one time nightly feed then you'll probably want Snapshot Replication.  If you want a more real time feed then you'll want to look at Transactional Replication.

Now replication doesn't support replicating the views, so you'll need to replicate the base tables, removing any columns which aren't needed by the website then create the views on the MySQL database.