Tear tree parts apart?

It is possible, it just depends on the level of realism you want to achieve. The simplest solution would be a tree consisting of already separated parts: trunk and branches. Each branch would need a Rigidbody set to kinematic for not falling off and that set to kinematic true just before applying forces to throw them off.
This will get a whole lot more complicated if you want the tree to incorporate with Unity's terrain, move it with the wind, or if you want to split a tree consisting of just one mesh at the start.