Best I could do. But it's destructive to the hash.

use strict;

my $HoA_ref = {'GAT' => [2, ['ttt',-3,1],['ttc',-3,3],['ccc',-1,2]],
               'AAA' => [13,['aaa',-1,2],['atg',-2,2]], 
               'TTT' => [11,['tta',-2,1],['atc',-3,3]]
               };


sub print_zHoA {
    my ($HoA) = shift;
    foreach my $mc (sort {$HoA->{$a}->[0] <=> $HoA->{$b}->[0]} keys %$
+HoA){
      print "$mc $HoA->{$mc}->[0]:\n";
      print join(',', map {$_->[0]} splice( @{$HoA->{$mc}}, 1)) . "\n"
+;
    }
}

print_zHoA($HoA_ref);
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I think the thing that was throwing you is that $x->[][] is syntactic sugar for $x->[]->[]. Another possible confusing point is that in your function, you are receiving a reference to a HoA rather than a HoA. So anywhere you use $HoA{$x} it should be $HoA->{$x}.