Change your handler to look for 'feature' elements, and use xpaths to scope down to your 'residue' elements:

my $xfile = <<EOF;
<sas_residue_annotation xmlns="http://url/Schema" xmlns:xsi="http://ww
+w.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://url/Sche
+ma test.xsd">
<features>
<feature>
<feature_name>feature_one</feature_name>
<residues>
<residue>
<residue_index>2</residue_index>
<residue_name>R</residue_name>
</residue>
<residue>
<residue_index>4</residue_index>
<residue_name>V</residue_name>
</residue>
</residues>
</feature>
<feature>
<feature_name>feature_two</feature_name>
<residues>
<residue>
<residue_index>5</residue_index>
<residue_name>S</residue_name>
</residue>
</residues>
</feature>
</features>
EOF

use strict;
use warnings;
use XML::Twig;

my $twig= new XML::Twig(
    twig_handlers => { feature => \&feature }
);

$twig->parse($xfile);

sub feature {
    my ($twig, $feat) = @_;
    if ($feat->first_child('feature_name')->text() eq 'feature_one') {
        for my $res ($feat->findnodes('residues/residue')) {
           my $res_idx  = $res->first_child('residue_index')->text();
           my $res_name = $res->first_child('residue_name' )->text();
           print "$res_idx $res_name\n";
        }
    }
}  

__END__
2 R
4 V
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