You want to delegate the ability to create and delete Office 365 User accounts as well as reset passwords.
Per TechNet, the best role for this is the User Management Administrator.
- Log into O365.
- Go to the Admin page.
- Click on Users->Active Users.
- Edit the user.
- Go to Settings.
- Set Assign Role to Yes and select the Role “user management administrator”.
- Click Save.
Be careful! The User Management role, while not a Global Admin, is still very possible. They can strip a User of a License that gives them email, etc.