If you have two RadGridView controls and you want to export both of the grids to a common file on two different sheets, it is suitable to use FileExportMode.NewSheetInExistingFile. However, when using the export overload to a stream doesn't respect the ExportMode.
Workaround: use exporting to a file:
string exportFile = @"..\..\exportedData.xlsx";
GridViewSpreadStreamExport spreadStreamExport = new GridViewSpreadStreamExport(this.radGridView1);
spreadStreamExport.FileExportMode = FileExportMode.NewSheetInExistingFile;
spreadStreamExport.ExportVisualSettings = false;
spreadStreamExport.RunExport(exportFile, new SpreadStreamExportRenderer());