Earlier quoted context omitted.
Mandrill is not "the backend service behind MailChimp". Mandrill came after MailChimp and is a separate thing - they only allow it to be used for transactional email. Sending a newsletter via Mandrill violates its Terms of Service.
I just went through Mandrill's TOS [0] and didn't see anything referencing a ban on emailing lists. From my understanding, and having used Mandrill for some time, it can be used for anything you want (that follows its double opt-in, no spam requirements). [0] https://mandrill.com/terms/
"Use Mandrill to send automated one-to-one email like password resets and welcome messages, as well as marketing emails and customized newsletters."
Emphasis on the "as well as marketing emails and customized newsletters" section there.
The difference of Mandril is that is doesn't have all the fancy features of Mailchip that people "would expect" to create a newsletter etc so Mandril is aimed at developers/software etc. That does not mean you can not use it for same uses as Mailchimp though.