"Throw you with a stone" vs "Throw a stone at you"

The difference is in the meaning implied by with.

With:

1.Accompanied by (another person or thing)

Ex: a nice steak with a bottle of red wine

2.Indicating the instrument used to perform an action:

Ex: cut the fish with a knife

When you say, I will throw you with a stone, the implication is throwing someone along with a stone(refer the first definition). On the other hand, when you say, I will cut you with a knife you mean that you will cut the person using the weapon of your choice, which in this case, is a knife(second definition).

The I will...you with was a good observation, though.

It all hangs on the meaning of to throw. It looks as though to throw can mean to hit in South Africa. You definitely can hit someone with a stone. But this is not a meaning you will find in dictionaries. The basic, conventional meaning of to throw is, quoting from Longman Dictionary:

1 Throw a ball/stone etc. [intransitive and transitive] to make an object such as a ball move quickly through the air by pushing your hand forward quickly and letting the object go

So, if you want to hit someone with a stone, you usually send a stone, not the person, flying through the air. If you’re on ship I suppose you could throw somebody overboard with a stone tied to them to make sure they sink. Or you could throw somebody off a horse with a stone, i. e., by hitting them with a stone.

This has to do with the difference between transitive and intransitive verbs. I think.

Transitive verbs require an object, whilst intransitive ones do not.

With transitive verbs, the first object, or whatever stands for an object (most often a noun or a personal pronoun), after the verb is most likely the object.

In "I'll throw you with a stone" the word "you" immediately follows "throw"; this means that "you" is the object of "throw"; which would imply that the speaker will hurl the interlocutor, after which said interlocutor, propelled by the force of the speaker's powerful throw, will have to travel some distance involuntarily, presumably through the air, and crash-land once the gravity and friction have worn down the initial force imparted to him or her by the act of throwing. The stone, then, serves as an instrument: the speaker intends to toss the interlocutor some distance with the help of that stone (possibly sling-shaped), in accordance with the prophecy.

Oh, and, by the way, despite the Biblical allusion, throwing rocks is more common than throwing stones these days. Hmm. That's not exactly accurate. Wait. Ah! I got it: stones are cast; rocks are thrown. Or hurled.

Conversely you'd need to come up with a very convoluted sentence to include "cut at you with a knife". Also "throw X at someone" is very different to "throw X to someone". Some verbs need a preposition in some sentences to make the meaning clear. It's the verb rather than the noun (weapon here) that makes the difference: you could "hurt someone with" a knife or a stone or other projectile.