Irrigation and nitrogen management are crucial for sustainable potato (Solanum tuberosum L.) production. A field experiment was conducted during the 2022 and 2023 growing seasons at Farmington, New Mexico, to evaluate the performance of two chip potato varieties (Lamoka and Waneta) under three irrigation regimes (full irrigation (FI), 20% deficit irrigation (DI) and 40% DI) and seven nitrogen fertilizer rates (0, 60, 115, 170, 220, 280, and 340 kg N/ha). The treatment combinations of irrigation regimes, nitrogen rates, and varieties were arranged in a split–split plot design with three replications as main plot, sub-plot, and sub-sub plot, respectively. The two-year results showed that irrigation regimes had the most significant effect on plant growth, physiology, and tuber yield of the potato varieties. For both Lamoka and Waneta, the plant height and canopy cover were lower under 40% DI than under 20% DI and FI treatments. The SPAD meter values were higher under 40% DI, followed by 20% DI and FI treatments, whereas the stomatal conductance was higher under FI, followed by 20% DI and 40% DI during both growing seasons. Regardless of nitrogen rates and variety, a 20% water-saving irrigation strategy reduced the total tuber yield by 4.5% and 22.1% in the 2022 and 2023 growing seasons, respectively, while the 40% water-saving irrigation strategy reduced total tuber yield by 36.8% and 58.2% in the 2022 and 2023 growing seasons, respectively, as compared to full irrigation. Shifting from full irrigation to 20% DI could save 711.2 to 1036.3 m3/ha of irrigation water. For Lamoka, the highest total tuber yield was obtained with 60 kg N/ha under 20% DI and 220 kg N/ha under FI in 2022 and 2023, respectively. For Waneta, the highest total tuber yield was obtained with 115 kg N/ha under 20% DI and 170 kg N/ha under FI in 2022 and 2023, respectively. Maximum water use efficiency (WUE) was obtained at 60 kg N/ha with 20% DI for both Lamoka and Waneta in 2022, while maximum WUE was obtained at 220 kg N/ha under FI for Lamoka and at 170 kg N/ha for Waneta in the 2023 season. The maximum nitrogen use efficiency (NUE) was achieved with 60 kg N/ha under 20% DI for both varieties during both growing seasons. Thus, for sustainable irrigation and nitrogen management, the application of a 20% deficit irrigation strategy with a lower nitrogen rate (60 to 170 kg N/ha) could be the best option to improve WUE and NUE with minimal tuber yield reduction. Our study suggested that 40% deficit irrigation would not be beneficial as compared to both full irrigation and 20% water-saving irrigation.