A fully validated inductively coupled plasma optical emission spectrometry (ICP-OES)–based method combined with a simplified sample preparation procedure for the determination of up to 15 elements (Al, Ba, Ca, Cd, Cr, Cu, Fe, K, Mg, Mn, Na, Ni, Pb, Sr, and Zn) in caffeinated yerba mate (YM) drinks was proposed. Various “green” treatments (acidification or dilution with a HNO3 solution and direct analysis of untreated YM with or without sonication (US)) that could replace the traditional total sample decomposition before spectrometric measurements were tested and compared. The key selection parameter was the analytical performance of the ICP-OES method obtained with each sample preparation procedure in terms of the precision and the trueness of results and limits of detection (LODs) of elements. It was found that the acidification of YMs with concentrated HNO3 to 5%, supported by US (10 min, room temperature (RT)), provided the best results, i.e., LODs at 0.11–8.5 ng g−1, precision below 5%, and trueness better than 5% (97.0%–105% as recoveries). Eleven YM drinks, commercially available on the Polish market, were analyzed with the proposed method. In addition to the mineral content, the concentration of caffeine in all analyzed YMs was determined and compared. Finally, the studies were completed by determining the bioaccessible fraction of selected elements and caffeine in YMs using in vitro gastrointestinal digestion (GID) in order to evaluate the nutritional value/risk assessment of these drinks. Accordingly, the bioaccessibility of nutritious elements (Ca, Fe, Mg, Mn, Zn) and caffeine was within 40%–59%. Except for Mn, it was established that by drinking daily 1 L of YMs, the recommended dietary intakes (RDIs) of the aforementioned essential elements were covered to a low degree (<4.5%). Hence, they are not an important source of these elements in the human diet. On the other hand, potentially toxic elements (Al, Ba, Sr) were found in a relatively inert form. Opposite to minerals, YMs can supply human organisms with quite high amounts of natural caffeine in bioaccessible form (31–70 mg per serving).