You are copying your texts a lot of times unnecessarily. You might try an array instead:

sub slow_match {
  my($hash_ref_1,$hash_ref_2) = @_;

  my @text_id = keys %hash2;
  my @text = values %hash2;

  while ( my($pattern,$high_lvl_id) = each(%hash1) ) {
    my $match = qr/\b$pattern\b/;
    for my $text_index (0..$#text) {
      if ($text[$text_index] =~ $match) {
         $$hash_ref_1{$text_id[$index_index]} .= ':'.$high_lvl_id;
         foreach my $part (split(/\s/,$pattern)) {
            $$hash_ref_2{$text_id[$text_index]} -> {$part} = 0;
         }
       }
     }
   }
}
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