  We develop a high order cut finite element method for the Stokes problem
based on general inf-sup stable finite element spaces. We focus in particular
on composite meshes consisting of one mesh that overlaps another. The method is
based on a Nitsche formulation of the interface condition together with a
stabilization term. Starting from inf-sup stable spaces on the two meshes, we
prove that the resulting composite method is indeed inf-sup stable and as a
consequence optimal \emph{a~priori} error estimates hold.
