Replace your grid_check() function with:

sub grid_check {
    my @f = grep { !$grid[$_] } 0 ..80;
    unless (@f) {
        return sudoku_print();
    }

    my @min = (1..9);
    my $idx = 0;
    for my $cntr (@f) {
        my %p = map { $_ => undef } 1 .. 9;
        foreach my $cell (@{$search{$cntr}}) {
            delete $p{ $grid[$cell] };
        }

        my @v = keys %p;
        if (@min >= @v) {
            @min = @v;
            $idx = $cntr;
        }
    }

    foreach my $val ( @min ) {
        $grid[$idx] = $val;
        grid_check();
    }
    return $grid[$idx] = 0;
}
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The problem? You were calculating waaaay too much for each iteration, particularly since you threw away most of it anyways. This much better represents what you were trying to do. The results? For the devilish one, I went from 37.XX seconds to 1.XX seconds on my Macbook Pro. It's actually faster than the other hard one (2.7X seconds for me). That just has to do with path selection. It could be sped up about another 5-10% with a couple little things here and there, but I think this is the major improvement.