In response to the problem of gas–liquid–solid three-phase flow in deep-sea hydrate extraction pipelines, a gas–liquid–solid three-phase flow model considering the dynamic decomposition of hydrates is established using continuity equations, momentum equations, and energy equations. The numerical solution of the theoretical model is achieved using the finite difference method. Comparing the theoretical model with the experimental results, the results showed that the average error of gas holdup, liquid holdup, solid phase content, gas phase velocity, liquid phase velocity, and solid phase velocity obtained from the theory and experiment are 8.24%, 0.41%, 1.88%, 5.80%, 2.81%, and 2.22%, respectively, which verified the correctness of the theoretical model. On this basis, the influences of hydrate abundance, liquid phase displacement, and wellhead backpressure on the gas–liquid–solid three-phase flow characteristics in the pipeline were investigated, and it was found that the gas holdup rate will increase with the increase in hydrate abundance, liquid phase displacement, and wellhead backpressure, with the influence of hydrate abundance being more sensitive. The liquid holdup rate increases with the increase in hydrate abundance and liquid phase displacement, but decreases first and then increases toward the wellhead position with the increase in wellhead backpressure. The solid phase content decreases with the increase in hydrate abundance, and first increases and then decreases toward the wellhead position as the liquid phase displacement and wellhead backpressure increase. The influence of gas phase velocity on the abundance of hydrates is relatively small, but it increases with the increase in liquid phase displacement. When the wellhead backpressure increases, the instantaneous increase then tends to flatten out. The influence of hydrate abundance on the liquid phase velocity is also relatively small, but it increases with the increase in liquid phase displacement and decreases with the increase in wellhead backpressure. The solid phase velocity will increase with the increase in hydrate abundance and liquid phase displacement, but it will not show significant changes with the change of wellhead backpressure. The research results can provide a theoretical basis for the safety of hydrate mining.