Cut to New Layer wasn’t that helpful in SL6, but this has been improved in SL7 : you now have two new actions, Cut to New Layer (improved) and Cut to Layer Below.
Cut to New Layer will cut any selected content to a new layer without leaving the active layer.
Cut to Layer Below [Shift+X] will cut any selected content to the layer below (in the layers list) without leaving the active layer.
So you can chain multiple selection+cut to below+selection+cut to below without ever leaving the active layer, and have the layer below receive all the data you selected and cut.
Similarly you now also have Copy to New Layer and Copy to Layer Below [Shift+C].