It helps if you post a complete runnable script

#!/usr/bin/perl
use strict;
use warnings;
use XML::Twig;
use Time::Piece;

my $file_to_read      = 'input.xml';
my @elements_to_treat = qw(node1 node2 node3);

delete_node(\@elements_to_treat);

sub delete_node {
   my ($all_elements) = @_;
   
   my %handlers;    
   for my $element (@$all_elements){
     $handlers{$element} = sub { $_->delete() };
   }
    
   my $dateLog = localtime->ymd('_');  
   my $file_to_write =  $file_to_read.'-parsed_'.$dateLog.'.xml'; 
   open my $fh_out, '>', $file_to_write 
      or die "Could not open $file_to_write : $!";
   $handlers{ '_default_' } = sub { $_[0]->flush($fh_out) };
   
   my $twig = new XML::Twig(
     twig_handlers => \%handlers,
     pretty_print  => 'indented',     
   );
   $twig->parsefile($file_to_read);
   close $fh_out;
   print "Created $file_to_write\n";
}
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