Abstract The seabed soil of the polymetallic nodule mining area is relatively thin, soft, and fluid, which will produce large deformation under external disturbance. Its undrained shear strength is related to strain-rate and strain-softening effect. It is an important engineering safety problem for the deep-sea mining vehicle (DSMV) to travel in the soft seabed, and its sinkage is a vital index affecting the traction performance. It is necessary to study the sinkage performance of the DSMV under the characteristics of large soil deformation, but there are only few existing studies. This study established a numerical model of seabed soft soil with Tresca constitutive considering strain-rate and strain-softening effects. First, a numerical simulation study was carried out on the interaction between the DSMV track plate and the seabed soil, and the influence of track plate structures on the pressure–sinkage characteristic was obtained. Then, a simplified three-dimensional model of the “PIONEER-I” DSMV was established. Under the condition of wet weight and initial vertical velocity, the influence of different initial bottoming velocities, weight, and soil parameters on the sinkage of the DSMV was obtained. An empirical prediction model of the DSMV sinkage was established based on the energy method and numerical calculation results.