Is this possible in Unreal 4?

I am wanting to make a game like this:

Mine is not a rotatable cube, but instead just a flat square, but the concept is similar. I started coding a template in which the player character (the cursor) can only move along the x and y axis, and when it crosses over a spot, that part of the box disappears. While this works, it is not the effect I am really wanting. I am wanting it to work more simillarly to the video where you draw a rectangullar section, and then that entire section disappears when it is “closed.” Is this possible to do in Unreal? If so, can someone point me in the right direction to make it work?

Realtime slicing just became a thing in 4.13, I’d check out the features livestream video and go from there.