To Mises the state is epitomized in its executive branch:
An anarchistic society would be exposed to the mercy of every individual. Society cannot exist if the majority is not ready to hinder, by the application or threat of violent action, minorities from destroying the social order. This power is vested in the state or government.
He even uses the same word I like: "crush":
State or government is the social apparatus of compulsion and coercion. It has the monopoly of violent action. No individual is free to use violence or the threat of violence if the government has not accorded this right to him.
The state is essentially an institution for the preservation of peaceful interhuman relations. However, for the preservation of peace it must be prepared to crush the onslaughts of peace-breakers. (HAn, 149)
Again, "the old Romans were more realistic in symbolizing the state by a bundle of rods with an ax in the middle," (719) clearly denoting the executive branch of the government. Neither in these passages nor, to my knowledge, anywhere else does Mises explicitly assign the tasks of law-making and arbitration of disputes to the government. On the contrary:
The total complex of the rules according to which those at the helm employ compulsion and coercion is called law.
Yet the characteristic feature of the state is not these rules, as such, but the application or threat of violence. (Omnipotent Government, 46)
So, Mises would hardly be opposed to privatizing, in full or in part, the other two branches.