You can delete your Atlassian account including all your product access (e.g. Jira Cloud, Bitbucket, etc.). See Atlassian account for users -> Delete your Atlassian account including an explanation what is exactly is deleted.
TL;DR: If you want your personal data erased, do not delete your Atlassian Account yet. Instead, make a General Inquiry so we can locate everything that should be removed.
Atlassian has published GDPR and You about your personal data rights under the new EU regulation. It has full details about what data Atlassian collects and how to remove it. For some things we will need to help you do this because the ability to self-serve has not yet been created.
Your Atlassian Account is the thing that connects all your personal data. If you remove it first, it will be much harder to help you exercise your right to access and erasure.
Update: That's a wrap! Thanks so much for your questions. If you didn't make it for the live AMA, not to worry. Add your questions below and I will get to them ASAP. Hello Atlassian Community...
Connect with like-minded Atlassian users at free events near you!Find an event
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no Community Events near you at the moment.Host an event
You're one step closer to meeting fellow Atlassian users at your local event. Learn more about Community Events