The determination of grape quality parameters is intricately linked to the mineral composition of the fruit; this relationship is increasingly affected by the impacts of climate change. The conventional chemical methodologies employed for the mineral quantification of grape tissues are expensive and impracticable for widespread commercial applications. This paper utilized Laser-Induced Breakdown Spectroscopy (LIBS) to analyze the mineral constituents within the skin, pulp, and seeds of two distinct Vitis vinifera cultivars: a white cultivar (Loureiro) and a red cultivar (Vinhão). The primary objective was to discriminate the potential variations in the calcium (Ca), magnesium (Mg), and nitrogen (N) concentrations and water content among different grape tissues, explaining their consequential impact on the metabolic constitution of the grapes and, by extension, their influence on various quality parameters. Additionally, the study compared the mineral contents of the white and red grape cultivars across three distinct time points post veraison. Significant differences (p < 0.05) were observed between the Loureiro and Vinhão cultivars in Ca concentrations across all the dates and tissues and for Mg in the skin and pulp, N in the pulp and seeds, and water content in the skin and pulp. In the Vinhão cultivar, Ca differences were found in the pulp across the dates, N in the seeds, and water content in the skin, pulp, and seeds. Comparing the cultivars within tissues, Ca exhibited differences in the pulp, Mg in the skin and pulp, N in the pulp and seeds, and water content in the skin, pulp, and seeds. These findings provide insights into the relationship between the grape mineral and water content, climatic factors, and viticulture practices within a changing climate.