Please examine the log files in C:\Documents and Settings\myUser\Application Data\Microsoft SQL Server Migration Assistant\YourProject\log\ssma.log folder. Change myUser by your user name on Windows. Application Data is a hidden folder.
Have you follow all the steps provided on this documentation?
If you are migrating big tables, please consider these adjustments.
UPDATE:
Based on the errors you found on the logs, llease make sure you are specifying the correct schema and database name to SSMA. Grant ALL PRIVILEGES and FLUSH PRIVILEGES to that login MNPalvelinanonymous user where the MySQL instance is installed.