Unfortunately, if the IP is blacklisted by CBL and Spamhaus you will likely run into issues. We are actively working to improve the reputation of IP addresses, but many of these services are slow to delist an IP once it has been blacklisted.
If you’re just attempting to send outgoing mail from the server, I strongly recommend using a service like Sendgrid or Mandrill. They both offer free tiers. If that’s not an option, you can recreate your droplet in order to pick up a new IP address. The system attempts to reserve the IP for you if you create a new droplet with the same name as the old one. So in order to ensure that you receive a new IP, create the new one before destroying the old one.
Regarding the blacklist itself, I could suggest contacting the DigitalOcean support team directly for further assistance.
As a side note, here is an interesting read on why you may not want to run your own mail server but rather use an SMTP provider:
When setting up a web site or application under your own domain, it is likely that you will also want a mail server to handle the domain's incoming and outgoing email. While it is possible to run your own mail server, it is often not the best option for a variety of reasons. This guide will cover many of the reasons that you may not want to run your own mail server, and offer a few alternatives.