No! Don't do this with your own hands. You can't kill him instantly without pain and without blood.
If you try to break his neck, very surely you won't know the correct moves which is needed for that, and you will cause only terrible pain for him. His neck is much stronger as you would think.
The surest way is if you take him to an animal ambulance and let him put to sleep forever. It is pain-free, although he will suffer on the way.
If you won't do that, then 1) stun him with a fist hit to his nape 2) cut his neck with a knife. This is the way of the rabbit killing for meat. Do it deeply and hard, and in a wide angle to surely cut the arteries. He will move a lot, so it is better if you do this with full of your strength. If you kill, do everything so strong as you only can, because his body will be much thougher as you would think. So, hit him so strong as you only can, and cut his neck so strong and deep, as you only can.
But the best is if you take him to a vet for euthanasia.
P.s. I know this because I worked some years as voluntary animal rescuer. During that I've seen multiple cats surviving sicknesses / wounds where as a layman I didn't ever thought they are survivable. Much earlier, as a child, I've also seen people killing household rabbits for meat (it has a technique which you surely won't reproduce on the spot).
Only a vet will be able to say, what to do, but they try to get the most possible money from you, and they also don't like to kill (and not only because an euthanasia is only around some tens of dollars while a costly treatment can go on hundreds of $s. But also because most of them is a vet and not a human doctor because he likes the animals). So, the optimal behavior if you take the rabbit to the vet for euthanasia, but if the vet is strongly against it, then you let him to convince you.
P.s.2. Most stray animal (i.e. which hasn't ever seen a human), if they can choose between a nearly-mortal wound and being yet another second around a human, chooses the first. If the rabbit is in your hands, his largest problem won't be his (mortal) wound, but that he is unable to escape from you. If you capture the rabbit, put it in a dark, closed thing, the best is a cat box with a blanked opening. So he will think he is hidden, and won't suffer from the fear from you.