A periodic pigging operation performed to clean off sediment and provide operators with detailed health information for a pipeline is mandatorily required. The research on pigging-induced issues for the steel catenary riser (SCR), one of the key parts in offshore hydrocarbon recovery pipelines between the floating production system and the seabed, has been scarce until now. As a result, there is an urgent need for theories to guide the pigging operation to ensure safe pigging is achieved in deepwater risers. In this paper, a study aiming to determine the effects of the pigging impact load and the pigging-induced slugging load on the dynamic response of the riser is reported. A SCR pigging model was established and proposed based on the finite element analysis (FEA) method. The stress distribution and displacement of the SCR were investigated under the pigging conditions, with the consideration of the effects of waves, currents, and floating platform movements. It was found that the pigging load has large effects on the stress and displacement of the touchdown zone (TDZ), especially the touchdown point (TDP). The displacement of the TDZ in the Y (vertical) direction is more significant than that in the X (horizontal) direction under pigging conditions, and the maximum displacement of the TDZ in the Y direction is proportional to the weight of the pig, as well as the length of the pigging-induced slugging.