The next statement you have is essentially useless -- it breaks out of the inner for-loop only, which means that the push is always executed. this could be resolved by using a label so that the next applies to the outer for loop, or by using a boolean flag, but consider a different approach -- a hash to provide a dictionary (grep would be natural, but inefficient in this case):

my %stopwords = map { $_ => undef } @stopwords;
$/=" ";
while(<>){
  chomp;
  push @lessWords, $_ unless exists $stopwords{$_};
}
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Update: An after-thought rewrite:

my %stopwords = map { $_ => undef } @stopwords;
$/=" ";
@lessWords = grep( exists $stopwords{$_},  map {chomp; $_} <> )
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