Your MySQL databases can be fully managed from the MySQL Databases page. To delete a database just go to Websites → Manage, search for MySQL Databases on the sidebar and click on it:
In the section List of Current MySQL Databases And Users, click on the options button (⋮) in front of the desired database and choose Delete:
NOTES:
Deleting a database is a non-reversible action. Instead of deleting the database, you can clear it with just a few clicks
You can download a backup of your database before deleting