Probably not. For instance MySQL does not support stored views plus the entire security regime is different. A better bet would be to use Enterprise manager to SQL that contained create statements for all of the tables and then use an ODBC connection to transfer the data from MSSQL to MySQL. This would at least allow you to transfer the data from one to the other.
Enterprise Manager is the software that comes with MS-SQL server that allows you to control and manage MS-SQL. If you have MS-SQL, you have Enterprise Manager. If you are using a website host who uses MS-SQL, you probably don't have Enterprise Manager. If this is the case, and your database isn't too complex, you can manually recreate your tables in MySQL and then use an ODBC connection to allow you to transfer data from the MS-SQL database to the MySQL database.