This did not work for me. All data was pasted into the first cell...
Try copying from Excel to Notepad and then copying again from Notepad to Sharepoint. I've been using this method for all sorts of things for a very long time. Often, wherever you copy from has additional formatting that may not be visible. Notepad doesn't support any special formatting, just plain text, so pasting onto there assures that any unnecessary formatting is removed.