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When you delete a document from the Manage tab, you are only deleting it from your view. In theory, there are other signatories that have a right to review that document, and no one of them can remove access for the others via the Manage tab.
Individual non-admin users may not truly delete an agreement in an ad-hoc fashion.
True document deletion comes in two forms:
Adobe Sign - Document Retention
Retention - an Enterprise process by which Adobe Sign automatically deletes the Files related to an agreement from the Adobe Sign servers after a defined amount of time. The Audit report is kept in the system to provide legal cover if the existing PDF copies of the agreement are ever contested.
Retention requires the account admins to sign a waiver affirming they understand that their documents are being deleted from the system, and are required to deliver a Signed And Filed email (with the attached signed PDF) to each recipient of the agreement, ensuring that all parties have a copy.
Adobe Sign - Feature: Deleting Agreements for Recipients GDPR
GDPR agreement deletion - The GDPR tools fully delete an agreement from the Adobe System, Files and audit trail included. To use the GDPR tools, you have to be a Privacy Admin on the account.