Here is Hans Hoppe's explanation of how Mises viewed the state...
Austrain Economics Newsletter (AEN): Was Mises better than the classical liberals on the question of the state?
HOPPE: Mises thought it was necessary to have an institution that suppresses those people who cannot behave appropriately in society, people who are a danger because they steal and murder. He calls this institution government.
But he has a unique idea of how government should work. To check its power, every group and every individual, if possible, must have the right to secede from the territory of the state. He called this the right of self determination, not of nations as the League of Nations said, but of villages, districts, and groups of any size. In Liberalism and Nation, State, and Economy, he elevates secession to a central principle of classical liberalism. If it were possible to grant this right of self-determination to every individual person, he says, it would have to be done. Thus the democratic state becomes, for Mises, a voluntary organization.
AEN: Yet you have been a strong critic of democracy.
HOPPE: Yes, as that term is usually understood. But under Mises's unique definition of democracy, the term means self rule or self government in its most literal sense. All organizations in society, including government, should be the result of voluntary interactions.
In a sense you can say that Mises was a near anarchist. If he stopped short of affirming the right of individual secession, it was only because of what he regarded as technical grounds. In modern democracy, we exalt the method of majority rule as the means of electing the rulers of a compulsory monopoly of taxation.
Mises frequently made an analogy between voting and the marketplace. But he was quite aware that voting in the marketplace means voting with your own property. The weight of your vote is in accord with your value productivity. In the political arena, you do not vote with your property; you vote concerning the property of everyone, including your own. People do not have votes according to their value productivity.
AEN: Yet Mises attacks anarchism in no uncertain terms.
HOPPE: His targets here are left-utopians. He attacks their theory that man is good enough not to need an organized defense against the enemies of civilization. But this is not what the private-property anarchist believes. Of course, murderers and thieves exist. There needs to be an institution that keeps these people at bay. Mises calls this institution government, while people who want no state at all point out that all essential defensive services can be better performed by firms in the market. We can call these firms government if we want to.