Have you copied something on the clipboard before pasting.. You need to do a cut or copy.. The following code demonstrates that..
Excel.Range R1 = (Excel.Range)oSheet.Cells[11, 11];
R1.Copy(Type.Missing);
Excel.Range R2 = (Excel.Range)oSheet.Cells[15, 15];
R2.PasteSpecial(Excel.XlPasteType.xlPasteValues, Excel.XlPasteSpecialOperation.xlPasteSpecialOperationNone, false, false);
The new code after your comments
Excel.Range FilterRange = xlWorkSheet.get_Range("A1", "X6100");
FilterRange.AutoFilter(6, "Project Leader", Excel.XlAutoFilterOperator.xlAnd, Type.Missing, true);
Excel.Range splRange1 = FilterRange.SpecialCells(Microsoft.Office.Interop.Excel.XlCellType.xlCellTypeVisible, Type.Missing);
splRange1.Copy(Type.Missing);
xlWorkSheet = (Excel.Worksheet) oWB.Worksheets.get_Item(2);
Excel.Range R1 = (Excel.Range)xlWorkSheet.Cells[1, 1];
R1.PasteSpecial(Microsoft.Office.Interop.Excel.XlPasteType.xlPasteValues, Microsoft.Office.Interop.Excel.XlPasteSpecialOperation.xlPasteSpecialOperationNone, false, false);