Collision of falling in the mechanical harvesting process of sweet potato is one of the main causes of epidermal destruction and damage to sweet potato tubers. Therefore, a sweet potato mechanical characteristic test and a full-factor sweet potato drop test were designed. Based on the analysis of the fitting mathematical model, the impact of the drop height, collision material and sweet potato chunk size on the damage of the sweet potato were studied. The mathematical models were established by fitting analysis of the IBM SPSS Statistics 22 software between the drop height and the sweet potato chunk size with each test index (impact force, impact stress, broken skin area and damaged area). The critical epidermal destruction height and the critical damage height of a certain size of sweet potato when it collides with a collision material can be calculated by the mathematical model, and the critical epidermal destruction mass and critical damage mass of sweet potato when it falls from a certain height and collides with a collision material can also be calculated. Then a series of critical values (including critical epidermal destruction force value, critical epidermal destruction impact stress, critical damage force value, critical damage impact stress) of mechanical properties of sweet potato were obtained. The results show that the impact deformation of sweet potato includes both elastic and plastic ones, and has similar stress relaxation characteristics. The critical damage impact stress of sweet potato is that the average value of the impact stress on the contact surface is less than it’s Firmness. The results provided a theoretical basis for understanding the collision damage mechanism of sweet potato and how to reduce the damage during harvest.