Your neighbor did nothing by accident. He wanted that tree cut down for a number of reasons...perhaps it was depositing leaves in his yard and gutters, maybe he wanted more sun light, perhaps he was fed up with the branches leaning over his yard, shading it. There could be a number of reasons, but trust me, people KNOW their property lines. It is those who ask for forgiveness, not permission who are the assaholics.
I had a 40' high climbing rosebush growing up my cedar tree IN my yard, on MY side of the fence. My neighbor, who is a young idiot, destroyed it when I was on vacation. He not only cut and pulled down my 23 year old climbing rose bush, he also cut up to twelve feet of cedar branches off of my tree. I was FURIOUS. That rosebush and tree provided me with excellent privacy and after he butchered it, I was left with a huge hole and a disgusting tree with stubs coming out of where he cut the branches and my rose bush was now just sticks, ankle high.
I told him if he did not restore my privacy I would sue him. He claimed he was clueless that the tree and rosebush were mine, but he HAD to come onto my property to cut it down, mind you, on MY side of the picket fence that supported the width of the climbing rosebush branches. Not even IN his yard, not at all.
I demanded that he put up a fence. He wanted $1200. from me, half of the cost. I told him to pound sand. He took his sweet time, over a year, to put up the fence. Finally, I had enough. I went out there with a low cut top, without a bra, and short, short, shorts. Finally one day, I heard his wife yelling at him to put up the damn fence!! LOL. Toooo funny.
Back to you......I would demand that he pay to have the stump removed and to buy and have a professional install a mature new tree, not a two foot sapling. I would first, call the police to report the incident.......remember, he trespassed on your property. You need to begin an evidence trail. Take photos. Take him to small claims court if you must. Neighbors need to realize they cannot do such idiotic things and get away with it.