Extreme weather events, such as severe droughts, pose a threat to the sustainability of beef cattle by limiting the growth and development of forage plants and reducing the available pasture for animals. Thus, the search for forage species that are more tolerant and adapted to soil water deficit conditions is an important strategy to improve food supply. In this study, we propose utilizing the mathematical concept of the Manhattan distance to assess the variations in the morphological variables of tropical forage grasses under water-limited conditions. This study aimed to select genotypes of tropical forage grasses under different water stress levels (moderate or severe) at this distance and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Nine varieties from five species were examined. Forage grasses were grown in 12-L pots under three soil irrigation regimes [100% pot capacity–PC (well-irrigated control), 60% PC (moderate drought stress), and 25% PC (severe drought stress)] with four replicates. Drought stress treatments were applied for 25 days during the forage grass tillering and stalk elongation phases. After exposure to drought stress, the growth and morphological traits of forage plants were evaluated. The results show that the use of the Manhattan distance combined with TOPSIS helps in the genotypic selection of more stable tropical forage grass varieties when comparing plants exposed to moderate and severe drought conditions in relation to the nonstressful environment (control). The ‘ADR 300’, ‘Pojuca’, ‘Marandu’, and ‘Xaraés’ varieties show greater stability when grown in a greenhouse and subjected to water stress environments. The selected forage varieties can be used as parents in plant breeding programs, allowing us to obtain new drought-resistant genotypes.