#! /usr/bin/perl
use strict;
use warnings;
# added:
use File::Spec::Functions qw( catdir );

my $dir = '/home/me/perl-stuff/";
my $mode = (stat $dir)[2];

# better use File::Spec::catfile
#$dir .= 'testdir';
$dir = catdir( $dir, 'testdir' );

mkdir( $dir, $mode ) or die "$!\n"; # update2: $mode added
chmod( $mode, $dir ) or die "$!\n";