Purely from a syntax point of view, the following would work:

my @res = grep { !/$tmp/ } @array;
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There is no good general way to negate a (Perl) regular expression. Negative lookahead/lookbehind like (?! and (?<! will easily fail for (say):

use 5.020;
use Data::Dumper;
my $tmp = qr/re/;

my @positive = grep {/$tmp/} 'rerere', 'foo';
my @negative = grep {/(?!$tmp)/} 'rerere', 'foo';

say Dumper \@positive; # 'rerere'
say Dumper \@negative; # 'rerere', 'foo'
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In the past, whenever I wanted this I've used an external variable for the grep result like this:

use 5.020;
use Data::Dumper;
my $tmp = qr/re/;

my $reverse = 0; # 
my @positive = grep {!! /$tmp/ xor $reverse } 'rerere', 'foo';
$reverse = 1;
my @negative = grep {!! /$tmp/ xor $reverse } 'rerere', 'foo';

say Dumper \@positive; # 'rerere'
say Dumper \@negative; # 'foo'
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