By "arguments to a subroutine", I'm referring to passing a special value that the subroutine could match against to determine what it should do. For example, below is a quick attempt to pull out your e-mail handling and move it to a separate function, along with how I might call it.

open( my $fh, "<", $array_ip_list )
  or send_mail("ip_list_error"),
    die "IP List File - nas_array_ip_list.txt not found";

# [ . . . Do lots of stuff here . . . ]

# If our external commands completed successfully, send our e-mail
if ($result_from_nas_check_function) {
    send_mail( "results", $filename );

    # [ Clean up after ourselves, delete our temp file, etc. ]
    exit 0;
}
else {

    # [ Notify e-mail that an error occured ]

    # [ Clean up after ourselves, delete our temp file, etc. ]
    die "Something went wrong.";
}
[download]

And here's an example of how I might define the send_mail() function, where I tell it what kind of e-mail it is sending, and then let it do the work:

# Expects at least 1 argument matching the type of e-mail to send, and
# optionally the additional arguments it might need.  If this got much
# more complicated, it might be worth passing the second argument as a
# hash to simplify multiple values coming in.
sub send_mail {

    # These could go at the beginning of your script, I just put them
    # here to make this a more complete example.
    use MIME::Lite;
    MIME::Lite->send( "smtp", "mail.server.com" );

    my $type = shift;    # what type of message should we send?
    my @args = @_;

    my $from = 'foo@example.com';
    my $to   = 'bar@example.com';
    my $msg;

    if ( $type eq "ip_list_error" ) {

        $msg = MIME::Lite->new(
                          From    => $from,
                          To      => $to,
                          Data    => "Error:nas_array_ip_list.txt:$!.$
+^E\n",
                          Subject => "IP List File - nas_array_ip_list
+.txt - "
                            . "Not Found For $0 Script on $ENV{COMPUTE
+RNAME}\n",
        );
    }

    elsif ( $type eq "results" ) {

        my $filename = $args[0];

        $msg = MIME::Lite->new(
            From    => $from,
            To      => $to,
            Subject => "Automated Check For NAS DataMover Health.",
            Type    => 'Multipart/mixed',

        );

        $msg->attach( Type        => 'TEXT',
                      Path        => $filename,
                      Filename    => $filename,
                      Disposition => 'inline', );
    }
    else {
        die "send_mail - bad type: $type\n"
    }

    # This will send our e-mail, regardless of which one we built.
    $msg->send;
}
[download]

Update: Added the final else, thanks to wfsp's excellent suggestion.