Salinity stress is a major constraint to sustainable crop production due to its adverse impact on crop growth, physiology, and productivity. As potato is the fourth most important staple food crop, enhancing its productivity is necessary to ensure food security for the ever-increasing population. Identification and cultivation of salt-tolerant potato genotypes are imperative mitigating strategies to cope with stress conditions. For this purpose, fifty-three varieties of potato were screened under control and salt stress conditions for growth and yield-related traits during 2020. Salt stress caused a mean reduction of 14.49%, 8.88%, and 38.75% in plant height, stem numbers, and tuber yield, respectively in comparison to control. Based on percent yield reduction, the genotypes were classified as salt-tolerant (seven genotypes), moderately tolerant (thirty-seven genotypes), and salt-sensitive genotypes (nine genotypes). Seven salt-tolerant and nine salt-sensitive genotypes were further evaluated to study their responses to salinity on targeted physiological, biochemical, and ionic traits during 2021. Salt stress significantly reduced the relative water content (RWC), membrane stability index (MSI), photosynthesis rate (Pn), transpiration rate (E), stomatal conductance, and K+/Na+ ratio in all the sixteen genotypes; however, this reduction was more pronounced in salt-sensitive genotypes compared to salt-tolerant ones. The better performance of salt-tolerant genotypes under salt stress was due to the strong antioxidant defense system as evidenced by greater activity of super oxide dismutase (SOD), peroxidase (POX), catalase (CAT), and ascorbate peroxidase (APX) and better osmotic adjustment (accumulation of proline). The stepwise regression approach identified plant height, stem numbers, relative water content, proline content, H2O2, POX, tuber K+/Na+, and membrane stability index as predominant traits for tuber yield, suggesting their significant role in alleviating salt stress. The identified salt-tolerant genotypes could be used in hybridization programs for the development of new high-yielding and salt-tolerant breeding lines. Further, these genotypes can be used to understand the genetic and molecular mechanism of salt tolerance in potato.