Objective: The deep-sea mining riser plays a crucial role in hydraulic lifting for mineral transportation. Unlike traditional oil production risers, which are fixed at both ends, the deep-sea mining riser features a bottom attachment connected to an intermediate storage chamber, creating a weak constraint boundary condition. During operation, the riser is subjected to the complex shear flow of the deep-sea environment, leading to vortex-induced vibrations and potential structural damage. Consequently, investigating the vortex-induced vibration characteristics of deep-sea mining risers with a free-bottom configuration under varying shear flow conditions holds significant engineering importance. Methods: A novel Wentzel-Kramers-Brillouin (WKB) method is proposed to analyze the static properties of a mining riser attached to an intermediate warehouse To examine the dynamic characteristics of the riser under the influence of the incoming flow, the wake oscillator model, in conjunction with the Runge-Kutta numerical method, is employed to compute the time-varying lift forces exerted on the riser by the external flow field. By integrating the WKB approach with the wake oscillator model, this work investigates the vibration behavior of deep-sea mining risers subjected to shear flow conditions. Results: (1) The analysis of varying shear parameters reveals significant trends in the vibration behavior of risers. As the shear parameters increase, the dominant vibration mode of the riser shifts to higher frequencies, indicating a change in the dynamic response of the riser. Initially, the displacement at the bottom of the riser decreases, likely due to the changes in the shear flow dynamics, before stabilizing at a certain value, suggesting a settling of the system's behavior over time. (2) When the maximum flow velocity of the shear flow increases, the riser's dominant vibration mode also rises, leading to an alteration in the vibration response. Modes adjacent to the dominant mode begin to have a more substantial impact on the overall vibration response. For modes of the same order, the displacement at the bottom of the riser increases initially, followed by a decrease, indicating a complex interaction between modes. However, a more substantial increase in the vibration response occurs when the mode transitions to a new one. (3) The study also highlights a new mode formation with a lower amplitude near the original dominant frequency before the vibration mode transitions. During this conversion, the amplitude of the initial accompanying mode increases, and a new mode emerges from the top of the riser, eventually reaching its peak amplitude. (4) A comparative analysis of deep-sea mining risers and traditional oil production risers shows that mining risers are more prone to exciting higher-order vibration modes. Risers with higher Young's modulus and larger length-to-diameter ratios tend to exhibit higher-order modes, with the dominant vibration mode increasing as the length-to-diameter ratio increases, while the response amplitude decreases. Conclusions: The impact of various shear flow parameters on the vibration response characteristics of deep-sea mining risers is systematically analyzed using numerical methods. Additionally, a comparative study between traditional oil extraction risers and deep-sea mining risers is conducted. This comparison offers valuable theoretical insights that can inform the design and optimization of actual deep-sea mining lifting system engineering.