How to tell a professor at a foreign university politely and impressively that I can’t cover the costs of living for my PhD?
As a prerequisite you would need to take care of your own funding to cover the costs of your entire PhD project (4 years, cost of living, housing etc.). If you have such funds I would be happy to discuss with you the possibilities.


This is the professor's polite way of saying, "We do not have funding to support you as a student.  If you obtain your own funding let's discuss further, otherwise there is little reason to continue this discussion."


  I don’t have any money to cover the cost of living. 


Then the appropriate response is, "Thank you for your time and consideration.  Please keep me in mind if a funded position opens up in the future."


  How can I answer him politely to impress him?


It sounds as though you'd like to respond in a way that causes him to allocate cost of living expenses to you.  I doubt the likelihood of that - if there are funded positions available, professors typically allocate them and notify students for them first, then once the positions are filled notify those that didn't make it that they have none available, and self funding would be the only option.  So chances are good that he simply has no funding to afford taking you on as an expense for their program.  It's also possible that they don't fund PhD students at all in their program.

However, if you have some knowledge that they do have funding and are simply not impressed enough by what you've presented so far to allocate some for you, then your options are limited.  You need to sell yourself and help them understand that your ability, talent, and skills are well above average and would be an asset to them that would be worth paying for.

How you would do that really depends a lot on your program and area of study.  Further, if you had more to show them, you should have done so well before this point.  Trying this now once they've already made their decision has a lower chance of success than impressing them when you first apply.

All that said, there's another option you might want to consider: bring your own funding with you.  It's not easy, but you may be able to write a successful grant proposal for them that gets them the funding they would need to fund the first part of your PhD.  You may have to do this a few times during your time there to continue your education.  Honestly, this method also has its risks, as they would have to cooperate, and they would have to allocate the funds received - not all of which would go to your education.

If this educational institution is particularly important to you and you have to get into their program, you might consider some of these options.  You might, instead, have a better chance with a different institution, though.  Lastly, it's reasonable to take a year or two off from education, get a job, and save money.  Industry experience in your field can be quite valuable to some PhD programs and might give you a leg up on the competition the next time you apply, and if not you should be able to bring some self-funding to the table.  In some industries you may be able to make contacts and network with people in a way that makes you more valuable.

Don't get too caught up in having what you want right now - getting a PhD later in life isn't a disadvantage.  It's more important to have good evidence - research, papers - of your skills than it is to have done it earlier.