I'm not sure I fully understand what you mean by "carve out", but I think you should use Tools > Boolean modelling menu :
- select all your objects and create a temporary object that matches the union of all these objects with Tools > Boolean modelling
- create a thin box around the objects
- select the union object and the thin box and use the option First - second or Second - first in Tools > Boolean modelling dialog
- hide or delete the union and the thin box