Isotropic soft magneto-rheological elastomers (s-MRE) are polymer-based composites where magnetically soft particles are randomly distributed in the elastomer matrix. Under a magnetic field, a strong modulus magnetic stiffening effect and a magnetostriction performance is exhibited for isotropic s-MRE, offering a wide application potential in vibration control, soft robotics and haptic displays. In the last decades, substantial theoretical work has focused on modelling the magnetostriction behaviour of isotropic s-MRE. Modelling the influence of magnetic fields to the viscoelastic behaviour of isotropic s-MRE has received less attention, despite the magnetic-dependent viscoelasticity is an essential component of the observed magneto-mechanical response and of great importance for the application of isotropic s-MRE. To predict the magneto-mechanical coupling behaviour accurately and provide guidance for the design of isotropic s-MRE-based applications, a multiplicatively-typed magneto-hyperelastic free energy and a new type of process-dependent viscosity evolution law is proposed in this work. Afterwards, the ability of the model to predict the modulus magnetic stiffening effect and magnetic-dependent nonlinear viscoelastic behaviour of isotropic s-MRE is examined. Finally, three sets of finite element case studies are presented to illustrate the feasibility of the model-based simulation and guide the design of isotropic s-MRE-related applications.