Salt stress adversely affects the growth and physiological relations in most tree fruit species. Little is known about genetic variation for salt tolerance, and the physiological mechanisms underlying salt tolerance in sapota (Achras zapota), an underutilized fruit crop valued for its nutritive and medicinal properties. Here, we examined the effects of saline (ECiw 4, 8, 12, and 16 dS/m) and sodic (RSC 2.5 and 5.0meq/l) water treatments on plant growth, physiology, and ion homeostasis in the different genotypes of Sapota. Although saline and sodic treatments appreciably reduced the plant growth (i.e., by 20–50%) compared to salt-free plants, genotypes ‘CSRS-13’ and ‘CSRS-15’ performed better than others. Salt-induced reductions in leaf area were indicative of the ability of sapota to better acclimatize to prolonged salinity stress by regulating the biomass production. Saline and sodic irrigation treatments increased the leaf Na+ and decreased the leaf K+; albeit with clear-cut genotypic differences. We observed better ion homeostasis in genotype ‘CSRS-17’ under salinity stress, and better physiological adaptations in genotypes ‘CSRS-11’ and ‘CSRS-17’ under sodicity stress. Principal Component Analysis revealed strikingly different responses of sapota genotypes to ‘low’ and ‘high’ salinity/sodicity treatments. Strong cultivar-specific responses to salinity and sodicity stresses evinced the existence of genetic variation for salt tolerance in sapota. Overall, our findings demonstrated the feasibility of sapota cultivation in areas with moderate sodicity (RSC ∼2.5 meq/l), and moderate-to-high salinity (∼8.0 dS/m).