.mdf equivalent for mysql (TOAD)
MYSQL usually comes with MyISAM/INNODB databases.  

For MyISAM the files are:

.MYD for data files
.MYI for index files
.frm for table format files    

InnoDB uses a single container file for the data and .frm for the definition and .ibd for the indexes. 

Are you trying to load data from SQL Server .MDF into MySQL DB? In simple words are you tring to migrate from SQL server to MYSql?  

Regards.