The title is self explanatory. Is there a way of directly doing such kind of importing?
The .bak file from SQL Server is specific to that database dialect, and not compatible with MySQL.
Try using etlalchemy to migrate your SQL Server database into MySQL. It is an open-sourced tool that I created to facilitate easy migrations between different RDBMS's.
Quick installation and examples are provided here on the github page, and a more detailed explanation of the project's origins can be found here.