In this talk, we present two cut finite element methods (CutFEM) for the numerical solution of the EMI (Extracellular-Membrane-Intracellular) model, with the goal of developing more efficient simulations of electric activity in explicitly resolved brain cell geometries. The EMI model is an example of a mixed-dimensional problem that couples an elliptic partial differential equation (PDE) on the extra/intracellular domains with a system of nonlinear ordinary differential equations (ODEs) over the cell membranes. Because of their complex geometry, generating volumetric meshes that conform to the brain cells is challenging. A way to remedy this problem is the cut finite element method, in which complex cell network geometries can be represented independently of the background mesh. Our method departs from an earlier developed Godunov splitting scheme for the model, which decouples the PDE part from the ODE part. For the PDE step, we apply two different CutFEM discretizations: a single-dimensional formulation with the intra/extracellular electrical potentials as unknowns, and a multi-dimensional formulation which also introduces the electrical current over the membrane as an additional unknown which formally results in a generalized saddle point problem with a penalty-like term. To discretize the ODE system posed on the unfitted membrane surface, we introduce a stabilized mass matrix approach. As part of our presentation, we provide numerical and theoretical evidence for the robustness and convergence properties of each CutFEM formulation. Finally, we test the complete splitting scheme for the fully-coupled model with convergence test and modeling the ODE-system with the Hodgkin-Huxley model. Our 3D test examples show that solving the EMI model using a CutFEM formulation is a promising approach for a simpler and more flexible handling of complex cell geometries.