This isn't really a scope question. The problem is: you can't store an array in a hash. You can store an arrayref though.

use strict; # important
use warnings; # important

my %debug; # you rarely want our (or local)

test_push(\%debug);

print "hey, it works: $_\n" for @{ 
        $debug{stack} # this probably contains our arrayref
        || [] # but if it doesn't, don't error out please
    };

sub test_push { # avoid camel case (imo)
    my ($debug) = @_;

    push @{ $debug->{stack} }, "lol";  # avoid unnecessary derefs

    # or

    my $ar = $debug->{stack};
    push @$ar, "lol2";

    return; 
}
[download]

Check out docs like perlreftut, perldata, perllol for further information.