You want to push a hash reference and not a hash:

push @filtered_responsearr, \%filtered_response;

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Your code can be greatly simplified in some other places:

   my $response = shift;
   my @fields;
   foreach my $a (0..$#_) {
      $fields[$a]= shift; }

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can be rewritten as a single assignment:

my( $response, @fields ) = @_;

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Likewise, copying the elements of %response into the filtered response can be done using a hash slice instead of the loop: 

@filtered_response{ @fields } = @response{ @fields }

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In reply to Re^3: Filter array of hashes for specific keys by Corion
in thread Filter array of hashes for specific keys by ddominnik

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