The trick is to first copy the sheets to a new workbook. So you would need something like:
    Dim oSh As Worksheet
    ThisWorkbook.Worksheets.Copy
    For Each oSh In ActiveWorkbook.Worksheets
        Application.DisplayAlerts = False
        oSh.SaveAs Filename:=FilePath, FileFormat:=xlCSV, CreateBackup:=False
        Application.DisplayAlerts = True
    Next
    ActiveWorkbook.Close False