Make sure you are logged in.
Now, go to https://www.zoosk.com/me/password-update and click “Deactivate your account”
Check the option “Permanently remove my account”
Confirm and you are gone!
For problems with the Zoosk Messenger or need other help, see https://zoosk.zendesk.com/home
Deletion of their Messenger goes the same way as any other software you wish to delete. Start > Configuration > Programs/Software/Delete a program, or the like.