  We consider a cut isogeometric method, where the boundary of the domain is
allowed to cut through the background mesh in an arbitrary fashion for a second
order elliptic model problem. In order to stabilize the method on the cut
boundary we remove basis functions which have small intersection with the
computational domain. We determine criteria on the intersection which guarantee
that the order of convergence in the energy norm is not affected by the
removal. The higher order regularity of the B-spline basis functions leads to
improved bounds compared to standard Lagrange elements.
