To reduce the structural vibration of the duct structure in pump-jet propulsors (PJPs) and lower the induced vibration noise, this study learned from the “processor box” in an aero-engine and set a certain number of axial slots in the PJP. First, using finite element analysis, both dry and wet modes of the PJP ducts with and without an axial slot structure were simulated for analysis. Next, with the two-way fluid–solid coupling calculation method, the vibration performances of the PJP ducts with and without axial slots were contrasted and studied. The differences in calculation results under different duct structures were compared from three aspects—the vibration displacement, velocity, and acceleration of the duct and mesh nodes. According to the present results, after the addition of axial slots, the vibration displacement, the vibration velocity, and the vibration acceleration can be significantly reduced, especially in the back segment of the duct. Meanwhile, it can be concluded that it is quite important to select vibration acceleration for structural analysis in evaluating the PJP vibration. This study can provide a reference for further designs of low-noise PJPs.