Mechanical properties of vegetables or crop materials play a noteworthy part in designing new related implements. These properties can be extracted from force–deformation curves. Several factors, such as soil preparation, irrigation, and pre- and post-harvest treatments influence them. The core objective of this investigation work was to analyze force–deformation curves obtained from compression, penetration, and shear tests of potatoes (Spunta cv.) produced with three tillage implements. The potatoes cv. Spunta were cultivated in loamy sand soil under the center-pivot irrigation system. The tillage implements used were a disc harrow plow, chisel plow, and moldboard plow. The trials were performed at a constant planting depth (15 cm) below the soil and a single plowing speed of 5.4 km/h. All data were expressed as an average of five replicates ± standard deviation. The force–deformation curves analysis showed that the modulus of elasticity for potatoes cv. Spunta ranged from 4.32 to 5.8 N/mm, the bioyield force ranged from 84.25 to 114.12 N, and rupture forces ranged from 100.90 to 139.78 N. Furthermore, the results showed that the average values of the elastic and plastic ranges were 3.0 and 2.1 mm, respectively. The mean value of hardness was 1671.53 N·mm. No significant differences were observed with respect to the two planting seasons, but tillage implements had a significant impact on the characteristics extracted from the compression tests. The mean of the maximum forces required to penetrate the potato during the penetration stage were 41.24 N, 44.86 N, and 47.16 N for potatoes produced with the disc harrow plow, chisel plow, and moldboard plow, respectively. Similarly, the means of the maximum forces required to cut the potato in the shear stage were 724.38 N, 761 N, and 773.43 N for the disc harrow plow, chisel plow, and moldboard plow, respectively. The force–deformation curves showed that additional information might be required to obtain a complete description of the potato quality necessary to harvest potatoes cv. Spunta using harvesting and handling equipment with reduced economic loss. An extensive study of the soil characteristics and the above-mentioned properties is also recommended. The results obtained about the mechanical characteristics of potatoes cv. Spunta can be useful in providing information that aids in designing potato harvesting machines and in potato products factories.