Calcular el total de días hábiles hábiles entre dos fechas

Si solo desea excluir los fines de semana, simplemente puede excluirlos usando un conteo condicional agregando:

count(distinct case when datepart(weekday, getdate()) <= 5 then date end)

Entonces su consulta se convierte en:

set datefirst 1;

select  count(distinct(dateadd(d, 0, datediff(d, 0,checktime)))) as workingdays,
        count(distinct case when datepart(weekday, getdate()) <= 5 
                            then dateadd(d, 0, datediff(d, 0,checktime)) 
                        end) as weekdays
from departments,
 dbo.USERINFO INNER JOIN dbo.CHECKINOUT ON 
     dbo.USERINFO.USERID = dbo.CHECKINOUT.USERID
where  userinfo.name='Gokul Gopalakrishnan' and deptname='GEN/SUP-TBL' 
and checktime>='2014-05-01' and checktime<='2014-05-30'

SIN EMBARGO Realmente recomendaría agregar un tabla de calendario a su base de datos. Hace que todo sea tan fácil que su consulta se convertiría en:

SELECT  DaysWorked = COUNT(cio.Date),
        WeekDaysWorked = COUNT(CASE WHEN c.IsWeekDay = 1 THEN cio.Date END),
        WorkingDaysWorked = COUNT(CASE WHEN c.IsWorkingDay = 1 THEN cio.Date END),
        TotalDays = COUNT(*),
        TotalWeekDays = COUNT(CASE WHEN c.IsWeekDay = 1 THEN 1 END),
        TotalWorkingDays = COUNT(CASE WHEN c.IsWorkingDay = 1 THEN 1 END)
FROM    dbo.Calender AS c
        LEFT JOIN
        (   SELECT  DISTINCT
                    Date = CAST(CheckTime AS DATE)
            FROM    dbo.Departments AS d
                    CROSS JOIN dbo.userInfo AS ui
                    INNER JOIN dbo.CheckInOut AS cio
                        ON cio.UserID = ui.UserID
            WHERE   ui.Name = 'Gokul Gopalakrishnan' 
            AND     d.deptname = 'GEN/SUP-TBL' 
        ) AS cio
            ON c.Date = cio.Date
WHERE   d.Date >= '2014-05-01'
AND     d.Date <= '2014-05-30';

De esta manera puede definir días festivos, fines de semana, etc. Es mucho más flexible que cualquier otra solución.

EDITAR

Creo que no entendí bien tu criterio original. Esto debería funcionar para usted sin tabla de calendario:

SET DATEFIRST 1;

DECLARE @StartDate DATE = '2014-05-01', 
        @EndDate DATE = '2014-05-30';

DECLARE @Workdays INT = 
    (DATEDIFF(DAY, @StartDate, @EndDate) + 1)
    -(DATEDIFF(WEEK, @StartDate, @EndDate) * 2)
    -(CASE WHEN DATEPART(WEEKDAY, @StartDate) = 7 THEN 1 ELSE 0 END)
    -(CASE WHEN DATEPART(WEEKDAY, @EndDate) = 6 THEN 1 ELSE 0 END);


SELECT  WorkingDays = COUNT(DISTINCT CAST(CheckTime AS DATE)),
        BusinessDays = @Workdays
FROM    dbo.Departments AS d
        CROSS JOIN dbo.userInfo AS ui
        INNER JOIN dbo.CheckInOut AS cio
            ON cio.UserID = ui.UserID
WHERE   ui.Name = 'Gokul Gopalakrishnan' 
AND     d.deptname = 'GEN/SUP-TBL' 
AND     cio.CheckTime >= @StartDate
AND     cio.CheckTime <= @EndDate;