The UN has a copy of the extradition treaty between the US and Brazil, the short version of it is that the treaty lays out in Article II an exhaustive list of crimes that are extraditable, skimming the list I don't see defamation (since of course in real life it's not a federal crime). As a general principle, Country A won't extradite someone to Country B if the conduct they are accused of in Country B is not a crime in Country A, if Country A does not think Country B would provide a fair trial, or if the person is convicted if the punishment likely to be imposed by Country B would be illegal under the laws of Country A (this comes up a lot with extradition from Europe to the US if a possible punishment for the crime is death). So in your hypothetical Brazil would probably be unwilling to extradite its own citizen for the crime the US accuses them of.
I think another part of your question is whether the US or Brazil would have jurisdiction over this defamation. In theory, both could claim jurisdiction over it. In practice most criminal conduct is criminal relatively universally, especially among similarly geolocated countries, so the rest of this paragraph is assuming both countries did consider the defamation criminal and extraditable. As a matter of judicial effectiveness an Internet crime would probably be prosecuted in the country where the person resides. There would likely be a language barrier too, if the US court would have to employ a Portuguese translator. However, this is all largely a political question more than a legal one, if the US really wanted to make an example of this person in their own country the US could try to use political leverage to get Brazil to extradite them. The US could also wait until the person travelled abroad and petition the third country to imprison and extradite them. That's something that happens more commonly for citizens of a country that the US does not have an extradition treaty with.