There is no automated way to remove, users have to contact support with a deactivation request on the support site (http://support.tango.me/anonymous_requests/new) and it will be deactivated.
One of our users points out: "It seems deactivation and not complete removal, because the mobile client said that the account was deactivated and I had to re-save my profile data to reactivate."
Publicly visible text/images often aren't properly deleted even when you succeed in deleting an account. Try editing or deleting them manually before deleting the account itself. If you're unsure what happens to your tracks you can always contact Tango.me and ask personally. By the way, deletion requests don't necessarily mean your data will actually be deleted (e.g. due to legal obligations).
If you signed up for Tango.me using a third-party login such as Facebook or Twitter, you probably want to revoke all access from Tango.me. Click the icon below to find out how.