Insert multiple times XML data (SQL SERVER)
One way is to insert all at once

INSERT INTO #tmpObject (tmpTagId,tmpObjectTypeId , tmpObjectId , tmpMode )
SELECT
    o.value ,
     ParamValues.item.value('objectTypeId[1]','INT'),
     ParamValues.item.value('objectId[1]','INT'),
     ParamValues.item.value('mode[1]','VARCHAR(16)')
FROM dbo.f_Split(@TagIdList,',')(@TagIdList,',') as o
     cross apply @ObjectList.nodes('objectList/object') AS ParamValues(item)



select * from #tmpObject order by tmpTagId


output:

tmpTagId    tmpObjectTypeId tmpObjectId tmpMode
----------- --------------- ----------- ----------------
1           1               654321      ADD
1           1               13456       ADD
2           1               13456       ADD
2           1               654321      ADD
3           1               654321      ADD
3           1               13456       ADD
4           1               13456       ADD
4           1               654321      ADD