You will only be deported to a country that the deporters know will accept you.
This will be the country you came from only if they know that you have permission to return there. You may sometimes ask to be deported to a specific country If You can demonstrate you have permission to enter, but in case of any doubt most countries will deport you to your country of citizenship.
If both countries are within the EU then you cannot start a second claim in the second country. They will send you back to the first country (which you cannot prevent) to continue processing. Since you have been rejected this means voluntary departure or deportation as described above. Theoretically you might volunteer to depart from second country rather than return to the first, but since you have already deceived them once you are going to be cut no slack.