To delete a site from emergence complete the following steps:
ssh into server and remove the applicable site directory - /emergence/mysitename (you'll need sudo privileges)
Remove the database from mysql using either pma or mysql command
Remove the mysql user for that database
Restart php using hostname:9083
You'll want to restart nginx too to completely flush out the old site's configuration, and you'll need to restart emergence-kernel before restarting either nginx or php
Removing the folder in /emergence/sql-backups will save some space too.