Their are 2 ways to delete contacts:

Tips:

Contacts can only be deleted from the archive list 

Only contacts that have not been on a membership may be deleted.

Deleting Contacts One At A Time:

If you want to delete a contact from another list you must change the contact to the archive list and then delete it.
You can change the contact group to archive by editing the client profile:
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Batch Deleting Multiple Contacts:

Ask Customer Support to turn on the "24 hour Batch Delete" rule.

Select the contacts and click "Batch Archive"

Go to the contact group "Archive"

---Select all the contacts and select "Delete Contact"