From the docs:

Whenever a particular entry becomes selected it stores a particular value into a particular global variable (as determined by the -value and -variable options for the entry).

You need variables for each group:

use strict;
use warnings;
use Tk;
use subs qw/menubar_etal/;

my ($g1,$g2);
my $mw = MainWindow->new;
$mw->configure(-menu => my $menubar = $mw->Menu(-menuitems => menubar_
+etal));

MainLoop;

sub menubar_etal {
  [
    map ['cascade',  $_->[0], -menuitems => $_->[1]],
    ['~Preference',
      [
        [qw/cascade Cascade1 -tearoff 0 -menuitems/ =>
          [
            map ['radiobutton', $_, -variable => \$g1],qw/1 2 3 4/,   
+                           
          ],
        ],

        [qw/cascade Cascade2 -tearoff 0 -menuitems/ =>
          [
            map ['radiobutton', $_, -variable => \$g2],qw/A B C D/,   
+                           
          ],
        ],
      ],
    ],
  ];
}
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