Deep-sea mining pipes are different from traditional ocean risers articulated at both ends: they are free-suspended, weakly constrained at the bottom, and have an intermediate silo at the end, compared to which relatively little research has been carried out on vortex-induced vibration in mining pipes. In this study, a sophisticated quasi-3D numerical model with two degrees of freedom for the flow field domain and structural dynamics of a deep-sea mining pipe is developed through a novel slicing method. The investigation explores how the vortex-induced vibrations of the mining pipe behave in various scenarios, including uniform and oscillating flows, as well as changes in the mass of the relay bin. The findings indicate that the displacement of the deep-sea mining pipe increases continuously as it moves from top to bottom along its axial direction. The upper motion track appears chaotic, while the middle and lower tracks exhibit a stable “8” shape capture, with the tail capturing a “C” shape track. Furthermore, with an increase in flow velocity, both transverse vibration frequency and vibration modes of the mining pipe progressively rise. Under oscillating flow conditions, there exists a “delay effect” between vibration amplitude and velocity. Additionally, an increase in oscillation frequency leads to gradual sparsity in the vibration envelope of the mining pipe in transverse flow direction without affecting its overall vibration frequency. Under the same flow velocity and different bottom effects, the main control frequency of the deep-sea mining pipe is basically unchanged, but the vibration mode of the mining pipe is changed.