Delete / DisAssociate Many to Many Relationship Record.

When you say DisAssocaiating a Many to Many Relationship Record, then you usually deattach the record, you won't delete the record.

Below function will DisAssocaiate a record. Here, you need to pass three parameter values
Parent Entity Guid,
Child Entity Guid, and
Relationship Name.

public bool DisassociateManyToManyEntityRecords(Moniker Moniker1, Moniker Moniker2, string strEntityRelationshipName)
{
    try
    {
        // Create a request.
        DisassociateEntitiesRequest request = new DisassociateEntitiesRequest();

        // Assign the request a moniker for both entities that need to be disassociated.
        request.Moniker1 = Moniker1;
        request.Moniker2 = Moniker2;

        // Set the relationship name that associates the two entities.
        request.RelationshipName = strEntityRelationshipName.Trim();
 

        // Execute the request.
        DisassociateEntitiesResponse response = (DisassociateEntitiesResponse)Service.Execute(request);

        return true;
    } 

    catch (SoapException ex)
    {
        return false;
    }
}