You probably use strict; and if you didn't, you should... That means (among some other things) that you must declare your variables with 'my' before using them (that's extremely useful against typos).
Something like this:

#!/usr/bin/perl

use strict;

# declare the variables

my $stopwords = "word";
my @data = qw( a word another and a verb a noun a phrase);

my @lessWords;

foreach my $word (@data) 
{ 
    if ($stopwords !~ / $word /) 
    {
         push @lessWords, $word; 
    } 


}
print "@lessWords\n";
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