The more yerba mate infusions that are consumed, the larger the amount of grounds generated. What is more, both the infusion and the residues after brewing remain rich elements. Therefore, a strategy for the three-stage assessment of the element content was presented. A new brewing method was based on dynamic extraction, ensuring both the ease of preparing the infusion and recovering the grounds. In turn, microwave-assisted acid mineralization was used to decompose the leaves and twigs of yerba mate before and after brewing. In total, 30 products were analyzed by ICP OES in three fractions each, i.e., dry yerba mate, infusion, and grounds, to determine up to 25 elements. The elemental composition was considered in terms of the country of origin, type, or composition of yerba mate. The extraction percentages obtained with dynamic extraction were comparable to previously used ultrasound-assisted extraction, as well as data from the literature. The three-stage strategy is a novel approach in yerba mate studies, and it may be a model procedure for the laboratory preparation of yerba mate grounds (waste that can be re-used, e.g., a natural fertilizer).