I'm not sure what that code is trying to do ... Tie::Handle is typically used as a base class, in which case your BLAH package should have this line after the use Tie::Handle; line:

our @ISA = qw(Tie::Handle);
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But even with that it looks like you're trying to have BLAH save to a scalar maybe? You pass in $output but never save it anywhere in the BLAH object you create. You then save the print data to a lexical scalar named $data that only the BLAH package can see. Maybe you mean something more like this (not tested)?

my $output = ''; # to store the output.

open SECOUT, ">&STDOUT";
tie *STDOUT, 'BLAH', \$output;

package BLAH;

use Tie::Handle;
our @ISA = qw(Tie::Handle);

sub TIEHANDLE {
    my $class = shift;
    my $save_to = shift;
    return bless({SAVE_TO => $save_to}, class);
}

sub PRINT {
    my $self = shift;
    ${$self->{SAVE_TO}} .= join '', @_;
}
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In other words, give the tie a reference to the scalar you want it to write to.