You need PATINDEX, try this:

IF OBJECT_ID('TempDB..#JobName','U') IS NOT NULL

DROP TABLE #JobName;

GO

--===== Create the test table

CREATE TABLE #JobName(

JobName NVARCHAR(100)

);

--===== Insert the test data into the test table

INSERT INTO #JobName (JobName)

SELECT 'InventoryCostReport_620013_SyteLine_HQ_App_Plt'

UNION ALL

SELECT 'Scheduling_3113457_SyteLine_HQ_App'

UNION ALL

SELECT 'ATP_CycleCountSummaryRpt_1792547_SyteLine_HQ_App'

UNION ALL

SELECT 'SCRM_EmployeeTardyReport_1301630_SyteLine_HQ_App'

UNION ALL

SELECT 'SPM_WarRoomReport_2695868_SyteLine_HQ_App'

UNION ALL

SELECT 'SP_WarRoomReportPastDue_3061579_SyteLine_HQ_App'

UNION ALL

SELECT 'TotalInventoryValuebyAcctReport_714769_SyteLine_HQ_App'

UNION ALL

SELECT 'VouchersPayableReport_3128272_SyteLine_HQ_App';

--==== SELECT the records

SELECT * FROM #JobName;

select left(JobName, patindex('%_[0-9]%', JobName) - 1) from #JobName;

drop table #JobName;

By the way, the code you posted doesn't work, I needed to make changes to get it to work.