I used the range operator approach like Athanasius but, to avoid keeping track of state, inside a grep feeding into a join with nuls then a couple of splits, one breaking the string into chunks between the 'D' and the 'M', the other inside a map breaking each chunk into an array ref.

use strict;
use warnings;

use Data::Dumper;

my @dd  = qw{ AA JJ CC M 1 1 3 4 D JJ 1 1 D M 3 3 4 D C M 3 3 3 D P Z 
+};

my @AoA =
   map { [ split m{\0} ] }
   split m{(?<=\0D)\0(?=M\0)},
   join qq{\0}, grep { m{^M$} .. m{^D$} } @dd;

print Data::Dumper->Dumpxs( [ \ @AoA ], [ qw{ *AoA } ] );
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The output.

@AoA = (
         [
           'M',
           '1',
           '1',
           '3',
           '4',
           'D'
         ],
         [
           'M',
           '3',
           '3',
           '4',
           'D'
         ],
         [
           'M',
           '3',
           '3',
           '3',
           'D'
         ]
       );
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A bit convoluted I suppose.