You could try to change the DISTINCT with GROUP BY. That might force it to eliminate duplicates before creating the XMLs (although, it doesn't seem like you need the DISTINCT at all).
The query is not complete, but I would suggest that you also try something like this:

SELECT IncidentReportIDs
FROM cmp.NotificationProduct NP

INNER JOIN(SELECT
      A.CompanyNotificationId,

      (SELECT DISTINCT IR.IncidentReportId, IR.DocumentNumber, IR.ReceivedDate
      FROM cmp.NotificationProduct NP
      INNER JOIN irp.IncidentProduct IP ON NP.IncidentProductId = IP.IncidentProductId
      INNER JOIN irp.IncidentReport IR ON IR.IncidentReportId = IP.IncidentReportId
      LEFT JOIN irp.IncidentCompanyBlocked ICB ON IR.IncidentReportId = ICB.IncidentReportId
      WHERE A.CompanyNotificationId = NP.CompanyNotificationId
      AND ICB.IncidentReportId is null
      AND NP.CompanyNotificationId IS NOT NULL
      FOR XML PATH('IncidentReport'), root('List')) AS 'IncidentReportIDs'
   FROM cmp.CompanyNotification A
   GROUP BY A.CompanyNotificationId
) E ON NP.CompanyNotificationId = E.CompanyNotificationId
WHERE ICB.IncidentCompanyBlockedId IS NULL
UNION ALL
SELECT BlockedIncidentReportID
FROM cmp.NotificationProduct NP
INNER JOIN(SELECT
      A.CompanyNotificationId,
      (SELECT DISTINCT IR.IncidentReportId, IR.DocumentNumber, IR.ReceivedDate
      FROM cmp.NotificationProduct NP
      INNER JOIN irp.IncidentProduct IP ON NP.IncidentProductId = IP.IncidentProductId
      INNER JOIN irp.IncidentReport IR ON IR.IncidentReportId = IP.IncidentReportId
      LEFT JOIN irp.IncidentCompanyBlocked ICB ON IR.IncidentReportId = ICB.IncidentReportId
      WHERE A.CompanyNotificationId = NP.CompanyNotificationId
      AND ICB.IncidentReportId is not null
      AND NP.CompanyNotificationId IS NOT NULL
      FOR XML PATH('IncidentReport'), root('List')) AS 'BlockedIncidentReportID'
   FROM cmp.CompanyNotification A
   GROUP BY A.CompanyNotificationId

) E ON NP.CompanyNotificationId = E.CompanyNotificationId
WHERE ICB.IncidentCompanyBlockedId IS NOT NULL;