Your MySQL databases can be fully managed from the MySQL Databases page. To delete a database just find Hosting → Manage → MySQL Databases:
In the section List of Current MySQL Databases And Users, click on ⋮ 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 always check for existing backups before deleting or even backing up your database as shown here: