The simple way is to write a code for sort which tells Perl how to compare two elements of the list:

#!/usr/bin/perl
use warnings;
use strict;
use feature qw(say);

my @strings = qw(xxxxxx.2012-50.yyyyy
                 xxxxxx.2012-51.yyyyy
                 xxxxxx.2012-52.yyyyy
                 xxxxxx.2013-1.yyyyy
                 xxxxxx.2013-2.yyyyy
                 xxxxxx.2013-3.yyyyy
                 xxxxxx.2013-4.yyyyy
                 xxxxxx.2013-10.yyyyy
                 xxxxxx.2013-11.yyyyy
                );

my @sorted = sort {
    my ($ay, $an) = $a =~ /\.([0-9]+)-([0-9]+)\./;
    my ($by, $bn) = $b =~ /\.([0-9]+)-([0-9]+)\./;
    $ay <=> $by or $an <=> $bn
} @string;

say for @sorted;
[download]

As this might be rather slow for larger lists, various technics exist to speed it up. One of them is called Orcish Maneuvre:

#!/usr/bin/perl
use warnings;
use strict;
use feature qw(say);

my @strings = qw(xxxxxx.2012-50.yyyyy
                 xxxxxx.2012-51.yyyyy
                 xxxxxx.2012-52.yyyyy
                 xxxxxx.2013-1.yyyyy
                 xxxxxx.2013-2.yyyyy
                 xxxxxx.2013-3.yyyyy
                 xxxxxx.2013-4.yyyyy
                 xxxxxx.2013-10.yyyyy
                 xxxxxx.2013-11.yyyyy
                );

my %cache;
my @sorted = sort {
    ($cache{$a} //= generate_key($a))
        cmp
    ($cache{$b} //= generate_key($b))
} @strings;

say for @sorted;

sub generate_key {
    my $s = (split /\./, shift)[1];
    my ($year, $number) = split /-/, $s;
    return $year . sprintf '-%03d', $number;
}
[download]

Update: Simple solution added.

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