G'day amitgsir,

There are a number of issues with your post:

• What does "UMI" mean? I'm guessing that's domain-specific jargon. You should explain this sort of thing in your post or, at the very least, provide a link to a definition.
• What does "2 mismatch" mean? Perhaps that's meaningful when "UMI" is explained.
• CLUSTER and DELIMIT:
  • Both are mentioned in your textual description.
  • Only CLUSTER appears in what I assume is your expected output.
  • Only DELIMIT appears in your code.
  • Only DELIMIT appears in your actual output (as a result of the last point).
• Using package variables for filehandles is a bad choice. Use lexical variables as shown in the open documentation.
• The token 'DATA' is special to Perl; see "perldata: Special Literals". Using this (or any other special token) in your code for something other than its intended purpose should be avoided. I've used it in my code example below so you can see normal usage.
• Don't comment out strict and warnings. Leave them in and fix the problems they highlight. If you don't understand the problem, or how to fix it, you can always ask here.
• I'm pretty sure chomping elements of the @ARGV array is unnecessary. You can test that with something like 'print "|$var|"', which will show terminal newlines (and any other unexpected or unwanted characters). Also note that, in my example code below, I haven't used chomp at all: consider whether removing newlines from input, then adding them back for output, is actually gaining you anything — it's often just a lot of redundant processing.
• Your code layout leaves much to be desired. Inconsistent indentation, and swathes of unnecessary whitespace, reduce readability. Choose a coding style that suits you and stick to it: "perlstyle - Perl style guide" has tips on how to do this.

The following code produces what I'm guessing is, at least, close to what you want. It produces the output in the same groupings you showshowed (see Update below), and it includes both the CLUSTER and DELIMIT tokens. Given the points I've already made regarding those tokens, this may not be exactly what you want: as stated, this is a guess on my part; modify to suit your needs.

#!/usr/bin/env perl

use strict;
use warnings;

use constant { COL0 => 0, COL2 => 1, ALL => 2 };

my ($col0, $col2) = ('', '');

print map {
    if ($col0 ne $_->[COL0]) {
        ($col0, $col2) = @{$_}[COL0,COL2];
        ("CLUSTER\n", $_->[ALL]);
    }
    elsif (substr($col2, 0, 3) ne substr($_->[COL2], 0, 3)) {
        $col2 = $_->[COL2];
        ("DELIMIT\n", $_->[ALL]);
    }
    else {
        $_->[ALL];
    }
}
sort {
    $a->[COL0] cmp $b->[COL0] || $b->[COL2] cmp $a->[COL2]
}
map {
    [ (split)[0,2], $_ ]
} <DATA>;

__DATA__
chrM:307    0   AGCGGGGA    129
chrM:307    0   AGCGGGGA    130
chrM:307    0   AGCGGGGA    129
chrM:308    0   AGCGGGGA    129
chrM:308    0   AGCGGGGA    130
chrM:308    0   AGCGGGGA    129
chrM:309    0   AGCGGGGA    129
chrM:309    0   AGCGGGGA    130
chrM:309    0   AGCGGGGA    129
chrM:307    0   TCAAAATG    130
chrM:308    0   TCAAAATG    130
chrM:309    0   TCAAAATG    130
chrM:307    0   TCACGGTG    130
chrM:308    0   TCACGGTG    130
chrM:309    0   TCACGGTG    130
chrM:307    0   TCAGCCTG    129
chrM:308    0   TCAGCCTG    129
chrM:309    0   TCAGCCTG    129
chrM:307    0   TCAGGGAG    130
chrM:308    0   TCAGGGAG    130
chrM:309    0   TCAGGGAG    130
chrM:307    1   TCAGGGTG    106
chrM:307    2   TCAGGGTG    130
chrM:307    2   TCAGGGTG    129
chrM:308    1   TCAGGGTG    106
chrM:308    2   TCAGGGTG    130
chrM:308    2   TCAGGGTG    129
chrM:309    1   TCAGGGTG    106
chrM:309    2   TCAGGGTG    130
chrM:309    2   TCAGGGTG    129
[download]

Output:

CLUSTER
chrM:307    1   TCAGGGTG    106
chrM:307    2   TCAGGGTG    130
chrM:307    2   TCAGGGTG    129
chrM:307    0   TCAGGGAG    130
chrM:307    0   TCAGCCTG    129
chrM:307    0   TCACGGTG    130
chrM:307    0   TCAAAATG    130
DELIMIT
chrM:307    0   AGCGGGGA    129
chrM:307    0   AGCGGGGA    130
chrM:307    0   AGCGGGGA    129
CLUSTER
chrM:308    1   TCAGGGTG    106
chrM:308    2   TCAGGGTG    130
chrM:308    2   TCAGGGTG    129
chrM:308    0   TCAGGGAG    130
chrM:308    0   TCAGCCTG    129
chrM:308    0   TCACGGTG    130
chrM:308    0   TCAAAATG    130
DELIMIT
chrM:308    0   AGCGGGGA    129
chrM:308    0   AGCGGGGA    130
chrM:308    0   AGCGGGGA    129
CLUSTER
chrM:309    1   TCAGGGTG    106
chrM:309    2   TCAGGGTG    130
chrM:309    2   TCAGGGTG    129
chrM:309    0   TCAGGGAG    130
chrM:309    0   TCAGCCTG    129
chrM:309    0   TCACGGTG    130
chrM:309    0   TCAAAATG    130
DELIMIT
chrM:309    0   AGCGGGGA    129
chrM:309    0   AGCGGGGA    130
chrM:309    0   AGCGGGGA    129
[download]

By the way, the construct I've used in the form of

... map { ... } sort { ... } map { ... } ...
[download]

is known as a Schwartzian Transform. It is particularly useful for sorting based on parts of a string while retaining the entire string, in an unmodified form, for eventual output.

Update: The original, expected output has changed. There is no notification of what changed or even that a change has been made. Here's the original (in the spoiler) that my response is based on: