Using this sample data:

CREATE TABLE #myTable (dt date UNIQUE NOT NULL);

WITH E AS (SELECT v FROM (VALUES (1),(1),(1),(1),(1),(1)) t(v))

INSERT #myTable

SELECT CAST(DATEADD(DAY, ROW_NUMBER() OVER (ORDER BY (SELECT 1))-1, '20140101') AS date)

FROM E a, E b, E c, E d;

You could do this:

SELECT [date] = MAX(dt),

[day] = DATENAME(WEEKDAY,MAX(dt))

FROM #myTable

WHERE DATENAME(WEEKDAY,dt) NOT IN ('Saturday', 'Sunday')

GROUP BY DATEPART(YEAR,dt), DATEPART(MONTH,dt)

ORDER BY MAX(dt); -- not required, including for readability