A simple way to save also is to use the clipboard and in 3 lines
Clipboard.SetDataObject(DataFormats.Text)
DataGridView.SelectAll()
IO.File.WriteAllText(Filename,DataGridView.GetClipBoardContent().GetText.Replace(vbTab, ","), System.Text.Encoding.ASCII)
sets the clipboard content to your desired DataFormat (Text)
select what you want to copy
(note:if you have filtered (invisible?) elements in your DGV they won't be copied)
Write the Clipboard content to the file
(note:here I have replaced the 'Tab' delimiter with a comma to get a CSV file)