I want to setup replication between SQL Server and MySQL, in which SQL Server is the primary database server and MySQL is the slave server (on linux).
Is there a way
No. At least not without doing a lot of dirty, bad things. MSSQL and MySQL speak different replication protocols, so you won't be able to set it up natively (which is the way you'd want to handle it). At best, you could hack together some sort of proxy that forwards insert/update/delete/create/alter, etc. queries from one to the other. This is a terrible idea as they don't speak the same SQL except in the most common case. Even database dumps which wouldn't really be replication are generally incompatible between vendors.
Don't do it. If you must use different OSes on your servers, standardize the database to something that runs on both.