Pipe-soil interaction is an essential aspect of a deep-water pipeline system. It may significantly influence both the structural behavior and integrity of the pipeline during installation and operation. The pipe embedment is an important factor influencing the pipe-soil interaction for an exposed pipeline. The embedment will determine the boundary conditions around the pipe for the subsequent loading scenarios. In this paper, based on the assumption of plane strain, the “Remeshing and Interpolation Technique with Small Strain” (RITSS) method was used to establish the large deformation finite-element model of vertical penetration of pipelines in clay. Compared with the previous literature, the robustness of the model was verified. Based on this model, the development mechanism of the soil shear band has been discussed during pipeline penetration; the effect of pipeline roughness on the undrained shear strength degradation mechanism and enhancement mechanism has been further explored. Finally, the effects of soil buoyancy, soil strength gradient, strain softening, and strain rate on the penetration resistance were discussed through parametric analysis. According to the influence sensitivity of each parameter, the evaluation framework of the penetration resistance has been developed. Compared with the previous literature, the validity of the framework was verified. The framework could provide guidance and reference for designing vertical penetration of pipelines in deep-water engineering.