If you take the definition of acronym as using the first one or more letters of the word, Russian does them a lot, and has done since Soviet times: Gazprom = Gazovaya promyshlennost, gas industry. German does them as well: Kripo = Kriminal-polizei. These syllabic acronyms (or syllabic abbreviations) were particular favourites of totalitarian regimes. From the Wikipedia article, I see Hebrew does them as well.
If you use non-initial syllables of a word, it becomes a Portmanteau. Portmanteaux don’t get used as abbreviations in English, but the Wikipedia article lists Indonesian for portmanteau acronyms. None of the other languages listed use portmanteaux in the same way.