The limited availability of phosphorus (P) in soils causes a major constraint in the productivity of potatoes, which requires increased knowledge of plant adaptation responses in this condition. In this study, six potato cultivars, namely, Agria, Lady Claire, Milva, Lilly, Sieglinde, and Verdi, were assessed for their responses on plant growth, leaf physiology, P use efficiency (PUE), and tuber quality with three P levels (Plow, Pmed, and Phigh). The results reveal a significant variation in the cultivars in response to different P availabilities. P-efficient cultivars, Agria, Milva, and Lilly, possessed substantial plant biomass, tuber yield, and high P uptake efficiency (PUpE) under low P supply conditions. The P-inefficient cultivars, Lady Claire, Sieglinde, and Verdi, could not produce tubers under P deprivation conditions, as well as the ability to efficiently uptake P under low-level conditions, but they were efficient in P uptake under high soil P conditions. Improved PUpE is important for plant tolerance with limited P availability, which results in the efficient use of the applied P. At the leaf level, increased accumulations of nitrate, sulfate, sucrose, and proline are necessary for a plant to acclimate to P deficiency-induced stress and to mobilize leaf inorganic phosphate to increase internal PUE and photosynthesis. The reduction in plant biomass and tuber yield under P-deficient conditions could be caused by reduced CO2 assimilation. Furthermore, P deficiency significantly reduced tuber yield, dry matter, and starch concentration in Agria, Milva, and Lilly. However, contents of tuber protein, sugars, and minerals, as well as antioxidant capacity, were enhanced under these conditions in these cultivars. These results highlight the important traits contributing to potato plant tolerance under P-deficient conditions and indicate an opportunity to improve the P efficiency and tuber quality of potatoes under deficient conditions using more efficient cultivars. Future research to evaluate molecular mechanisms related to P and sucrose translocation, and minimize tuber yield reduction under limited P availability conditions is necessary.