Cutting objects and letting them fall "naturally"

Thanks for the reply, we’ve moved a bit now - when we saw how the object looks like inside.

However, now we’ve bumped into a known problem (DEF-521) Scaling Collision Object when Game Object is scaled (DEF-521)

Is there, perhaps, a workaround on our specific problem if the bug isn’t dealt with yet?

To simplify the problem:

We have a tree object, “standing” upwards, the player should be able to cut it (straight horizontal line) and the chopped-off piece (rectangle shaped) should fall down to the ground.

P.S. We needed scaling only by Y axis