The alternate method that will solve the hole issue is to create a large cube (call this the cutter), do a boolean difference between your obj and the cutter.

After the boolean operate the cutter and the obj nodes are still in the outliner and can be keyframed. You can move, scale, and rotate them.

Below I create a sphere (the obj to be cut), and a cube (the cutter) and then do a boolean difference. Note they do not intersect at all to begin. This is important as if you start out with an intersection you can get artifacts and odd behavior if you if pull the cutter out of the obj.

Then I select the cutter from the outliner switch the move mode (w-key) to local and you can see the boolean is updated in real time and the hole that you'd get using the cut method is filled.

https://youtu.be/Mas3zm5U214