The way I read the PDF is that there is no mutation. The ink cloud is the creature's ability that it can use whenever it wants.
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This would make sense if the formatting of the ability matched every other ability. It doesn't. Instead the ability has bold text (like all other mutations) but is phrased like a monster ability (which never has bold text).
I ruled that it would be a once per rest ability when a player got it as a mutation. The players cannot get any sand from the squid's puppet as it is already dead. The ability itself is a double edged sword as no one can see through it. This struck me as a reasonable compromise.
The monster sounds like a cool idea, but its text is definitely wrong.