I don't think the Earth is structurally sound enough for that to work, at least if you're hoping to make any kind of a hollow shell. If the goal is just to pre

I don't think the Earth is structurally sound enough for that to work, at least if you're hoping to make any kind of a hollow shell. If the goal is just to preferentially remove the dense stuff first, that would likely work. You'd still destroy every part of the biosphere though. The crust bits shifting into place as you remove everything below them would be catastrophic, off the scale earthquakes everywhere and extreme heating and volcanic activity.