To avoid or mitigate global warming, several ocean carbon capture and storage concepts have been proposed. One of the recent approaches is to dispose carbon dioxide via a fixed vertical cantilevered pipe onto the seabed in deep waters. Due to a high aspect ratio and flexibility of such long pipe conveying fluid with fixed-free end conditions and external hydrodynamic loading caused by currents, the pipe may experience large-amplitude 3-D vibrations leading to structural failure. Hence, it is essential to understand and investigate the pipe nonlinear dynamic behaviors subject to combined flow-induced vibration (FIV) and vortex-induced vibration (VIV). In this study, the 3-D nonlinear equations of a cantilevered pipe discharging fluid in the sea are analyzed using a Galerkin-based multi modal approach combined with a finite difference Houbolt's integration scheme. Particular attention is paid to the combined effects of FIV and VIV on the dynamic response of the cantilevered pipe in water. To model the fluctuating lift and drag forces associated with VIV, the two dimensional wake oscillators distributed along the pipe are adopted. Numerical simulations in the FIV case of a pipe discharging fluid in the air are first validated with experimental results in the literature to justify the mathematical models and numerical approaches. Modal convergence analysis is also performed. Results in the combined FIV and VIV cases are then highlighted in order to show the effects of cross-flow and in-line VIV when compared with the pure FIV case. The effects of geometric nonlinearities, the coupling/interaction of multi modes and the space-time modifications of pipe responses and trajectories are highlighted. It is hoped that the numerical observations and findings obtained from this study could be verified by experimental studies which are presently lacking in the literature.