Note the mkdir documentation states:

"To recursively create a directory structure, look at the make_path function of the File::Path module."

for example:

#!/usr/bin/perl
use strict; 
use warnings;

use File::Path qw(make_path);

my $x='x'; 
my $y='y'; 
my $dirname = "$x/$y";

make_path( $dirname , {
    chmod => 0777,
});

my $output="$dirname/z.txt"; 
open ( my $fh, ">", $output ) or die "Cannot open file '$output': $!\n
+"; 

print $fh "\n It's ok.\n"; 

close $output;   
print "\n Program is over.\n";
[download]

Results:

D:\code>perl path.pl

 Program is over.

D:\code>cd x/y
D:\code\x\y>dir
 Volume in drive D is Data
 Volume Serial Number is 3241-B96B

 Directory of D:\code\x\y

22/04/2017  10:39    <DIR>          .
22/04/2017  10:39    <DIR>          ..
22/04/2017  10:39                13 z.txt
               1 File(s)             13 bytes
               2 Dir(s)  107,416,027,136 bytes free

D:\code\x\y>cat z.txt

 It's ok.

D:\code\x\y>
[download]