Here is my code

use strict;
use warnings;
use DBIx::Connection;
use DBIx::PLSQLHandler;

my $Datasource = "dbi:Oracle:sid=dev;host=10.11.12.13";

my $connection = DBIx::Connection->new(
        name     => 'dev',
        dsn      => $Datasource,
        username => 'scott',
        password => 'tiger',
);

my $plsql = $connection->plsql_handler(
            plsql      => "DECLARE
                            TYPE group_type IS RECORD
                            ( h1 groups.HANDLE_GROUP%TYPE,
                            g1 groups.GHANDLE%type);
                            group_rec group_type;
                            CURSOR data_groups IS
                            SELECT DISTINCT ghandle
                            FROM groups;
                            BEGIN
                            OPEN data_groups;
                            FETCH data_groups
                            INTO group_rec.g1;
                            WHILE data_groups % FOUND
                            LOOP
                            SELECT handle_group
                            INTO group_rec.h1
                            FROM groups
                            WHERE ghandle = group_rec.g1
                             AND rownum < 2;
                            DBMS_OUTPUT.PUT_LINE(group_rec.g1 || '==>'
+ || group_rec.h1);
                            :h2 :=group_rec.h1;
                            :g2 :=group_rec.g1;
                            FETCH data_groups
                            INTO group_rec.g1;
                            END LOOP;
                            CLOSE data_groups;
                            END;"
);

my $result_set = $plsql->execute();

print Dumper($result_set);
[download]

The above code is returning only one record, but when I execute my procedure in SQL Developer it is outputting many records

Any problem in my procedure...though

Usually when working with DBI and things interacting with it, the result from ->execute() only indicates success or failure. I presume you're supposed to ->fetch (or ->fetchall_arrayref) the results.