For the first time, the bioaccessibility of the mineral nutrients in ripe table olives and their contributions to the recommended daily intake (RDI), according to digestion methods (Miller’s vs. Crews’ protocols), digestion type (standard vs. modified, standard plus a post-digest re-extraction), and mineralisation system (wet vs. ashing) were studied. Overall, when the standard application was used, Miller’s protocol resulted in higher bioaccessibilities of Na, K, Ca, Mg, and Fe than the Crews’ method. The modified protocols improved most of these values, but the Crews’ results only approximated the Miller’s levels in the case of Na and K. The bioaccessibility of P was hardly affected by the factors studied, except that the modified Miller’s protocol led to higher levels when ashing. No significant effect of the mineralisation system was found. The modified Miller’s protocol, regardless of the mineralisation system, led to the overall highest bioaccessibility values in ripe olives, which were: Na (96%), K (95%), Ca (20%), Mg (73%), Fe (45%), and P (60%). Their potential contributions to the RDI, based on these bioaccessibilities and 100 g olive flesh service size, were then 29, 0.5, 4, 3, 33, and 1% respectively. The investigation has led to the development of a method for assessing the bioaccessibility of the mineral nutrients not only in ripe but also in the remaining table olive presentations and opens a new research line of great interest for producing healthier products.