SQL Server 2012 version above,
SELECT format(Closing_Date,'yyyy-MM') as ClosingMonth,
Category,
COUNT(Status) TotalCount
FROM MyTable
WHERE Closing_Date >= '2012-02-01'
AND Closing_Date <= '2012-12-31'
AND Defect_Status1 IS NOT NULL
GROUP BY format(Closing_Date,'yyyy-MM'), Category;