Deleting a Global Aurora RDS Cluster in AWS is a process that must be followed in a certian order in order to not run into issues. To better understand the process to use, it's important to talk about the layout first.

For Global RDS clusters, AWS doesn't simply make one mysql cluster that spans the two. It first creates a global definition and then creates individual clusters for each region. After getting that setup, it creates instances to work each cluster and then usese DB parameter groups to define what to do between them. There's a separate DB Parameter group for the Clusters themselves, as well as the instances. Our example has a cluster in both us-east-1 and us-west-2 and the removal goes as follows:

Remove your local cluster from the global one:

aws rds remove-from-global-cluster --profile <privileged_profile_name> --region us-west-2 --db-cluster-identifier <west_2_cluster_arn> --skip-final-snapshot

Find your list of instances for this region:

aws rds describe-db-instances --profile <privileged_profile_name> --region us-west-2 

Delete each one:

aws rds delete-db-instance --profile <privileged_profile_name> --region us-west-2 --db-instance-identifier <instance_id_found_above>

Delete the local cluster:

aws rds delete-db-cluster --profile <privileged_profile_name> --region us-west-2 --db-cluster-identifier <west_2_cluster_arn> --skip-final-snapshot

Do the other cluster:

aws rds remove-from-global-cluster --profile <privileged_profile_name> --region us-east-1 --db-cluster-identifier <cluster_arn> --skip-final-snapshot
aws rds describe-db-instances --profile <privileged_profile_name> --region us-east-1 
aws rds delete-db-instance --profile <privileged_profile_name> --region us-east-1 --db-instance-identifier <instance_id_found_above>

Delete each local cluster:

aws rds delete-db-cluster --profile <privileged_profile_name> --region us-east-1 --db-cluster-identifier <east_1_cluster_arn> --skip-final-snapshot
aws rds delete-db-cluster --profile <privileged_profile_name> --region us-west-2 --db-cluster-identifier <west_2_cluster_arn> --skip-final-snapshot

Delete the global cluster:

aws rds delete-global-cluster --profile <privileged_profile_name> --global-cluster-identifier <global_cluster_id>

If your not recreating this, you may want to also clean up your db parameter groups, cluster parameter groups, option groups and subnets using the commands (most of these you can remove the last argument and swap the word 'delete' with 'describe' in the command name to see a current list of what you have left:

aws rds --profile <privileged_profile_name> --region us-east-1 describe-db-parameter-groups
aws rds --profile <privileged_profile_name> --region us-east-1 delete-db-parameter-groups --db-parameter-group-name <parameter_group_name>
aws rds --profile <privileged_profile_name> --region us-east-1 delete-option-group --option-group-name <option_group_name>
aws rds --profile <privileged_profile_name> --region us-east-1 delete-db-subnet-group --db-subnet-group-name <subnet-group>