Another way of saying this in SQL is to use IN-lists. They may sometimes be more easy to interpret:
SELECT *,convert(varchar,DOJ,103) as DateOJ
FROM Registration_Mstr R,
Designation_Mstr D,
Department_Mstr DP
where R.DesgId = D.DesgId
and DP.DepartmentId = R.DepartmentId
and EmployeeStatus = 1
and D.Designation NOT IN('Administrator','Directors')
order by EmployeeName