In this paper, a modeling approach for strongly coupled Fluid-Structure Interaction (FSI) simulations of a mixing vessel stirrer is presented and discussed. A finite-volume Computational Fluid Dynamics (CFD) model is used to calculate the mixer flow field while the structural dynamics of the stirrer is based on a 2-DOF damped spring-mass oscillator system. The time integration of the stirrer response is carried out using the Newmark method, and is applied in conjunction with the implicit time integration of the fluid governing equations. The solution methodology employs a transient rotorstator interface to handle frame change between the rotor system and the baffles. Furthermore, mesh adaption around the rotor system is applied using an Arbitrary Lagrangian Eulerian (ALE) treatment of the fluid governing equations. The fluid forces acting on the impeller are analyzed and a method is proposed for extracting the added mass, damping, and stiffness coefficients, which are of significance in rotordynamic analysis. The computational results for the average stirrer deflections are in close agreement with experimental data, and the trends in the extracted rotordynamic coefficients align with other previously reported data for turbomachinery.