$Text::Wrap::columns = 60;
my $text = wrap('', '', $smstext);
print $text,"\n";
[download]

for this i have remove lines greater than 2 in $text

To extract just 2 lines, you can do $top2 = $text =~ /^(.*\n.*\n)/;

You can avoid unnecessary work in Text::Wrap if you limit the string you submit to it to a bit over the absolute maximum length of 2 lines together (your text says 140 characters, indeed a bit over 2x60 + 2 for the newlines), because the rest will be cut off anyway.

my $smstext = "This sentence will have more than 120 characters and i 
+want to truncate this string into two lines containing 60 characters 
+each and ignore characters above 140 in length" ;
use Text::Wrap;
local $Text::Wrap::columns = 60;
my($text) = wrap('', '', substr($smstext, 0, 140)) =~ /^(.*\n.*\n)/;
print $text;
__END__
Output:
This sentence will have more than 120 characters and i want
to truncate this string into two lines containing 60
[download]

Maybe substitute

$smstext =~ s~^(.*\n.*\n)~wrap('', '', $1)~e;
[download]

print "Now using Wrap method \n";
$Text::Wrap::columns = 60;
my $text = wrap('', '', $smstext);
my @chunks = split(/\n/,$text); # split $text into chunks
print $chunks[0]."\n".$chunks[1],"\n"; #take first two lines
[download]

Using Text::Wrap module is the better way. Here is the solution without using that module.

#! /usr/bin/perl

my @arr = split("", $ARGV[0]);
my ($i, $len) = 0;
my $newlines='';
my $maxlen = 60;
while ($i <= length($ARGV[0])) {
        $str1 = $str1 . $arr[$i];
        my $len = length($str1);
        if ($len == $maxlen) {
                if ($str1 =~ /\S+$/) {
                        $str1 =~ s/\s+(\S+)$//;
                        $newlines .= $str1 . "\n";
                        $i = length($newlines)-2;
                        $str1= "";$len=0
                } else {
                        $newlines .= $str1 . "\n";
                        $str1 = "";$len=0
                }
        }
        $i++;
}
print "$newlines\n";
[download]

Since other modules might be using Text::Wrap, it's a good idea to localise your change to $Text::Wrap::columns. This ensures that other modules aren't affected by your change to this variable.

local $Text::Wrap::columns = 60;
[download]

Kudos to bart for already mentioning this in their response.