The Galerkin difference method is a type of finite element methods where Lagrange shape functions are piecewise but span over multiple cells. With this, it allows to choose time-step sizes in explicit temporal methods independently of the polynomial order of the shape functions, which is a strong benefit compared to the standard finite element method, where the time-step sizes need to be reduced with increasing polynomial degree to maintain stability. This property has been proven to be valid for advection and wave equations. In this work, we extend the methodology for the linear advection equation on immersed domains, i.e., consider cut Galerkin difference methods. We analytically and numerically show that Galerkin difference methods are applicable to immersed domains and time-step sizes are comparable to the uncut case, i.e., are independent of the polynomial order.