Your question is a little unclear but my guess from your partial output is that you want something like this.

use strict;
use warnings;

use 5.010;

my @arr = qw{ A C D D C D A G F };

my $str = join q{}, @arr;

say for
   sort
   map { substr $str, $_ }
   0 .. length( $str ) - 1;
[download]

The output.

ACDDCDAGF
AGF
CDAGF
CDDCDAGF
DAGF
DCDAGF
DDCDAGF
F
GF
[download]

I hope I have guessed correctly and that this is helpful.

Update: A version that works on array subscripts rather than offsets into a joined string, using the revised data in the OP.

use strict;
use warnings;

use 5.010;

my @arr = qw{ a c a a a c a t a t z };

my @sortedIndices =
   map  { $_->[ 0 ] }
   sort { $a->[ 1 ] cmp $b->[ 1 ] }
   map  { [ $_, join q{}, @arr[ $_ .. $#arr ] ] }
   0 .. $#arr;

say join q{}, @arr[ $sortedIndices[ $_ ] .. $#arr ]
   for 0 .. $#sortedIndices;
[download]

Outputs

aaacatatz
aacatatz
acaaacatatz
acatatz
atatz
atz
caaacatatz
catatz
tatz
tz
z
[download]