The problem doesn't seem to be the -w, but rather that $In_Mente is forgotten. -w is always complaining about uninitialized-whatsoever, so we'll just have to make some precautions:

sub add($$) {
    my ($Val1, $Val2) = @_;
    my ($Result, $Tmp) = ('',0);
    my $In_Mente = '';
    (length($Val1) < length($Val2)) ? ($Val1, $Val2)=($Val2, $Val1):0;
    while (length($Val2) || length($Val1)) {
        $Tmp = substr($Val1,-1,1);
    $Tmp += substr($Val2, -1, 1) if (length($Val2));
    $Tmp += $In_Mente if (length($In_Mente));
        if ($Tmp > 9) { $In_Mente = 1; $Tmp -= 10;}
        else { $In_Mente = ''; }
        $Result = $Tmp . $Result;
        substr($Val1, -1, 1) = '';
        substr($Val2, -1, 1) = '';
        my $FResult = $Result;
        last if ($In_Mente eq '' && !length($Val2));
        }
    $Result = $In_Mente . $Result;
    $Result = $Val1 . $Result;
    return $Result;
    }

$a = '99999999999999999999999999999999999999999999';
$b = '1';
print "  $a\n+ $b\n= ", add($a, $b);
[download]

Prints out:

  99999999999999999999999999999999999999999999
+ 1
= 100000000000000000000000000000000000000000000
[download]