I have a site in which I create about two or three new pages by day.

Right know on my sitemap I'm putting the main urls, but now I decided to put the articles also.

So, my idea would be to add each url, and then the other day delete them and add the other urls. I know that google goes to my sitemap at least once a day. I would delete the old to don't overcharge my sitemap.

Would that make the browsers delete that articles that im erasing from the sitemap from their databases?

I think that no.. but I want to be sure.

Other thing that comes to my mind is that I could create another sitemap and put all the urls without deleting them. And remain with the old sitemap having only the main urls.

what would you recommend?

if you will remove some URLs from sitemap that would not affect their indexing status, but it's recommended to keep them in sitemap anyway.