I think that your first map and the subsequent sort in the ST look a little confusing. There is no need for an AoA as a simple anonymous list will suffice with no need for double subscripts in the sort block. Also, you can use split without arguments here as splitting $_ on whitespace is the default.

use strict;
use warnings;

my $discard = scalar <DATA> for 1 .. 2;

# Use the line below instead of above if
# you want to retain the column headers.
#
# print scalar <DATA> for 1 .. 2;

print
   map  {$_->[0]}
   sort
   {
      $a->[1] cmp $b->[1] ||
      $a->[2] cmp $b->[2] ||
      $a->[5] cmp $b->[5]
   }
   map  {[$_, split]}
   <DATA>;

__END__
Col1      Col2         Col3  Col4     Col5         Col6
========================================================
D1001     SNAM1        1     101      XYZ1234      21.11
D1001     SNAM1        1     102      XYZ2234      22.12
D1002     SNAM2        1     201      PQR2234      12.12
D1002     SNAM2        2     202      PQR2234      32.12
D1002     SNAM2        3     203      PQR2234      52.12
D1002     SNAM2        4     204      PQR2234      37.12
D1001     SNAM1        2     103      XYZ1234      22.12
D1003     SNAM3        1     301      ABC1234      22.12
D1002     SNAM2        5     205      PQR2234      37.12
D1001     SNAM1        4     104      XYZ1234      22.12
[download]

Cheers,

JohnGG