See the section "Building an XML filter" of XML::Twig. Here's a quick implementation:

use XML::Twig;
open my $ofh, '>', $output_filename or die $!;
XML::Twig->new(
  twig_print_outside_roots => $ofh,
  keep_spaces => 1,
  twig_roots => {
    book => sub {
      my ($twig, $book) = @_;
      if ($book->first_child_text('title') eq 'Title of Book 1') {
        $book->flush($ofh);
      }
      else {
        $book->purge;
      }
      return 1;
    }
  },
)->parsefile($input_filename);
close $ofh;
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