The documentation seems fairly explicit. You could show us some code, but that would spoil the fun of extracting the relevant information piece by piece from you.

So, my next question is, is it a mineral?

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.