This paper presents two new numerical methods for incompressible fluid/thin-walled structure interaction problems using unfitted meshes. The spatial discretization is based on different variants of Nitsche's method with cut elements. The degree of fluid-solid splitting (semi-implicit or explicit) is given by the order in which the space and time discretizations are performed. For the semi-implicit schemes, energy-based stability and a priori error estimates are derived and which guarantee the unconditional stability and optimal accuracy in the energy-norm of one the methods. Stability and a priori error estimates are also derived for one of the explicit schemes. Numerical experiments in a benchmark illustrate the performance of the different methods proposed.