I want to start promoting my sites by articles and I have one question.
Is it useful for the sites SEO to send the same article to many article directory sites? Does Google regard this as spamming? Thanks.
Nope, your extra entries will only be omitted and wherever your top ranking article is will show up. It’s good practice to some extent(if its your own content), but it can also be wasteful.
It’s not better to submit the same article to different article directories.
No problem you can send the same article in multiple sites.
Yes - you can also use an article spinner to slightly change the article for different websites.
In my opinion I would slightly change each article (as suggested above) for the different directories.
However, the value of the links you obtain by submiting your article to irrelevant directories has decreased greatly. Your much better of to guest blog for a relevant high authority website.
A brilliant article that is published on high traffic website will do wonders, but spammed across across numerous articles sites will have proportionally less effect.
article spinning would be perfect 
Article spinning is one of the big red flags in terms of potential spam articles. Do you really think that with all the intelligence behind the Google algorithm that they can’t detect article spinning?
Submitting your unique and valuable articles to multiple directories isn’t going to hurt your ranking. You will probably get a backlink from each directory although it’s debatable how much that link is really worth. However, if you spin your articles it looks spammy and you could be doing more harm than good.