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You trade for it by getting some high runes and making a game with the name "HRs 4 Beast Cryptic Axe" and then sitting there for several days, since nobody has something like that. I don't know why you would want something like that. If you want a weapon for the Necro to hold, HOTO's actually better. But if you want an aura weapon for the Necro to hold, then you should get Beast in a Berserker Axe (if you want to use it on other characters) or a War Axe or any other normal axe capable of getting 5 sockets (if you don't want to pump Str on the Necro).
If you want a weapon for the merc to hold, Infinity's better.
I'm not sure if I'm spoiling the fun for NoisemakerArrow, but my fingers are itching too much: The actual reason why there are no Beast cryptic axes is that a cryptic axe is no axe, but a polearm, despite the name, so you cannot make Beast out of it anyway.
Beast would make a pretty good merc weapon if it existed. Infinity might be more useful for minions because it reduces enemy defense and Beast doesn't reduce the cooldown time between their attacks, but Beast involves just a single HR and would provide more benefits to the merc himself (they don't have that cooldown time).