Your pattern seems alright, you just need to include the multiline modifier m, so that ^ and $ match line beginnings and endings as well:
/^\s*\n/gm
Without the m, the anchors only match string-beginnings and endings.
Note that you miss out on UNIX-style line endings (only \r). This would help in that case:
/^\s*[\r\n]/gm
Also note that (in both cases) you don’t need to match the optional \r in front of the \n explicitly, because that is taken care of by \s*.
As Dex pointed out in a comment, this will fail to clear the last line if it consists only of spaces (and there is no newline after it). A way to fix that would be to make the actual newline optional but include an end-of-line anchor before it. In this case you do have to match the line ending properly though:
/^\s*$(?:\r\n?|\n)/gm