I would say that your example is probably over simplistic, so I've expanded on and cleaned it up slightly:

<library>
 <book>
  <book1>Book1</book1>
  <title>Title of Book 1</title>
  <genre>Fantasy</genre>
 </book>
 <book>
  <book2>Book2</book2>
  <title>Not the Title of Book 1</title>
  <genre>Fantasy</genre>
 </book>
</library>
[download]

Now that we have something that's a little bit easier to show off some stuff, here's an example that does exactly what you ask.

use strict;
use warnings;
use XML::Twig;
use Data::Dumper;
my $DATA = '
<library>
 <book>
  <book1>Book1</book1>
  <title>Title of Book 1</title>
  <genre>Fantasy</genre>
 </book>
 <book>
  <book2>Book2</book2>
  <title>Not the Title of Book 1</title>
  <genre>Fantasy</genre>
 </book>
</library>
';

my $source_twig = XML::Twig->new('pretty_print' => 'indented');
$source_twig->safe_parse($DATA);

foreach my $book ($source_twig->root->children('book')) {
  if ($book->first_child('title')->text() ne 'Title of Book 1') {
    $book->cut()
  }
}
$source_twig->print();
[download]

And it's output:

<library>
  <book>
    <book1>Book1</book1>
    <title>Title of Book 1</title>
    <genre>Fantasy</genre>
  </book>
</library>
[download]