The global %hash is being altered because you are making alterations to its reference. What you want to do is dereference it in mysub(), like so:

#!/usr/bin/perl

use strict;
use warnings;
use Data::Dumper;

my %hash = (a => 1, b => 2);
mysub(\%hash);
print Dumper(\%hash);

sub mysub {
  my $h = shift;
  my %new_hash = %$h;
  delete($new_hash{'b'});
}
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You can do whatever you want to %new_hash and nothing will happen to %hash.