A computational study of the penetration of a blade into the core of an initially columnar vortex in an incompressible viscous fluid and the subsequent cutting of the vortex is reported for the case where the blade axis is initially orthogonal to the vortex axis. The vortex is advected toward the fixed blade by a free-stream velocity oriented tangent to the blade chord, where the free-stream speed is sufficiently large that the vortex does not induce ejection of vorticity from the blade boundary layer prior to impact of the vortex core with the blade leading edge. A range of computations are performed for cases both with and without ambient axial flow in the vortex core. As the blade leading edge penetrates into the vortex core, cross-diffusion between the columnar vortex and the blade boundary layer causes vortex lines originating in the columnar vortex to rapidly reconnect to those in the blade boundary layer. This cutting process is found to be always incomplete however, due to a change in sign of the spanwise vortex-induced velocity along the leading edge as the vortex is cut, leaving a thin vortex sheet that wraps around the blade leading edge. Cutting of a vortex with non-zero axial flow causes an asymmetry that results in an impulsive lift force on the blade. This lift force has maximum magnitude during the time period where the blade leading edge penetrates into the vortex core. Both the vortex cutting process and the unsteady lift force on the blade are found to be approximately independent of Reynolds number for the various cases examined.