How to make a destroyable landscape?

So I want to allow my character to be able to dig and deform the landscape in-game, like it is done in 7 Days To Die or Minecraft. How would I do that. Is it even possible using blueprints only?

No, not is not. That requires engine modification to work properly.

It is possible if you are good in C++ - try looking for codes when the editor deforms the landscape, and use the code inside your game.