Ähm, you want the contents of the $cleanHtml variable? Or you want to know how to read the contents of a file?!
Your code revised:
use warnings;
use strict;
use HTML::Normalize;
my $norm = HTML::Normalize->new;
open(my $in, '<', 'index.html') or die "Could not read 'index.html': $
+!";
my $dirty = do { local $/; <$in> };
close $in or die "Could not close: $!";
my $cleanHtml = $norm->cleanup(-html => $dirty);
open(my $out, '>', 'output.html') or die "Could not open 'output.html'
+: $!";
print $out $cleanHtml;
close $out or die "Could not close: $!";
-- Frank