Shlomo Sand's work has not been discredited in the sense that it was a widely accepted historical work that someone else "revealed" to be false.

The problem is, as the Guardian and Times Higher Ed pieces make fairly obvious, Sand's work is primarily about Jewish identity, not necessarily history. Its intent is more to undermine the factual basis of the Israeli national mythology than to advocate any particular historical view (I don't want my wording to mislead here--"undermine" is not necessarily negative, particularly if the myths are false, and "myths" are not necessarily false). They are not reviews by historians in journals of reviews by historians or history texts. As such, its positions on specific questions must be dealt with separately, rather than as one historical argument.

The big point a lot of people "get" out of The Invention of the Jewish People is the theory that Jews are primarily descended from the Khazars, a Medieval Turkic group that may have converted in part to Judaism. Sand is not the first person to write about this. There are papers and books about this concept that are intended primarily as works of history. This just isn't one of them. For the purpose of this answer I'm going to assume you're talking about Sand's views on Jewish ancestry, rather than the other historical topics his texts discuss (like I said, discussing a historical argument is not the point of the book).

Anyway, at the time it was written the Khazarian hypothesis was already out there, and not widely accepted. The book massively increased general knowledge of it, but does not seem to have altered the views of many historians. Evidence for Khazars converting at all is scant, and evidence that they all converted is even scanter (basically only one Muslim chronicler who said that the Khazars are entirely Jewish). There is further no solid evidence that they migrated north to become the Jewish population of Eastern Europe. While it's possible Khazars converted in large numbers, and possible many of their descendants still are Jews today (either from Eastern Europe or the Caucuses), the extreme versions of this, the "all Ashkenazim are Khazars" version, is pretty unlikely.

A related thesis is that Jews from areas besides Eastern Europe (and some in Eastern Europe) are primarily descended from converts from the Roman era. Again, this is definitely possible--there is some evidence that Judaism was much more active in converting in late antiquity and in the early middle ages than in later medieval or modern eras. But the thesis that Jews today are primarily descended from these converts lacks evidence for such a strong claim.

Where things get close to being discredited are genetic studies, undertaken after The Invention of the Jewish People, show that while modern Jews have substantial non-Levantine DNA, there is also substantial Levantine DNA, pointing to significant Levantine origin. This pretty decisively disproves the strong thesis of Sand's work, that Jews are entirely not Levantine (except the one study by Elhaik, but it is contradicted by more studies and the issue seems to be in his puzzling choice for a "Khazar control". The fact that a "Khazar control" should suggest that he went in looking for evidence of the Khazarian hypothesis, not asking the question of "what is the genetic origin of modern Jews"). Sand himself has dismissed this evidence for no real reason. So while it is possible that a weaker version of Sand's theses in this regard are accurate (that Khazars converted to Judaism and are part of modern Jewish ancestry, and that conversion to Judaism forms a larger-than-generally-accepted part of Jewish ancestry from the Roman era), the versions Sand has are not.

But, Sand's theses in this regard did not have a whole lot of evidence or widespread acceptance in the historical community before the DNA evidence. But again, this is not really the point of Sand's research. His goal is not to prove a historical event or events, it is to discuss a historical narrative's use in politics. While that it an interesting discussion, it is not really a historical view that can be discussed and proven or disproven by other historical works. Many of Sand's views are shared with other historians who've written about it in a more history-focused way, and those have never been widely accepted either.

I'll add to /u/gingerkid1234's response here by saying that the idea that Eastern European Jews are primarily descended from Khazars is not backed up by genetic studies at all. That hypothesis, put forward by others before him and popularized by Sand in his 2008 book, The Invention of the Jewish People, doesn't line up with genetic studies at all.

For example, this genetic study notes no evidence that this theory is correct. This theory has been largely discredited, at the end of the day.

Thank you very much for your responses. I did realise that his work was, at least in part, written to counter the racial ideology and theories that were developed to justify the establishment of the state of Israel, and the apparent necessity to dispossess materially and morally the indigenous inhabitants. I realise that he sought to show that modern Israelis were not descended from the original population of Judea or ancient Israel, and that the idea of a Jewish "race" is a modern construct. I can see why this would make some modern Israelis annoyed! I can also see why this might be supported uncritically by anti-semites!