The website says that, and then doesn’t give a source. I found this article. And Israel has admitted that this has happened in the past, in the 1990s, but hasn’t happened in a while, so this isn’t some baseless claim of pure defamation—there is fact behind it.
But I can’t find any articles on the subject that are propaganda. The only ones I can find about Israeli organ harvesting are like this one: reporting facts, not speculation. Regarding political cartoons, if you’re going to judge their journalistic integrity on cartoons, that would mean almost every news organization would have a bias. Better still, the bias changes from day to day depending on the cartoon! (Which haven’t been updated since 2008, and I’m not even sure are hosted on the site anymore. In any case, I can’t find the organ harvesting cartoon, so I don’t think it was Al Jazeera.)
Al Jazeera is a respected news organization that happens to be in the Middle East. When studying controversies surrounding Al Jazeera, many claim it is anti-Israel, and does that surprise you? A mainly Arabic news organization reporting in the Middle East being accused by Israel of not being pro-Israel enough? The shock. Israel does this all the time, as do its allies. Any criticism of Israel is labelled anti-Semitism when it is simply not.
Moreover, the U.S. claims an anti-American bias, the Russians claim Al Jazeera is too pro-American. Other controversies read the same way. Al Jazeera reports something negative, and people claim that it is a bias against them. In any case, the evidence for it being a propaganda machine is slim to none. Biased, maybe if not probably, but every news organization has a bias. But propaganda? No.