Awaiting for your comments harsitha..
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or let me know the challenges you're facing to implement the above logic..
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invoke the same batch in Finish method.

global void finish(Database.BatchableContext BC){
Database.executeBatch(new sampleBatch,1000);
}

To get External ID from outside sales force Environment

1. Either you have to hit their API via soap/Rest API call or
2. you have to provide them the login creds of your org and Object API name along with External Id API name as defined in sales force.

for option 1 : you can write your own Integration code to check for the External Id null… Read more

Write a batch class to delete the records.

Two ways of Executing the batch class :

1. Execute it in "Anonymous" block or
2. Create a VF page with a Delete button which invokes the batch class(with VF page you can catch the errors while performing delete operation and can show it on VF page as error messages)