The book appeared at Rinteln in 1631 without its author's name, which was a rational precaution: it accused named practices, and by implication the judges and princes who ran them, of killing the innocent by the hundred. Spee's authorship became known during his lifetime nonetheless, and it was affirmed later in the century by Leibniz, who admired the book. It was reprinted and translated into German, and it circulated among exactly the readers it was aimed at.
What it achieved is a genuine question rather than a settled one. Historians credit the Cautio Criminalis with contributing to the ending of witch prosecutions in several German territories, and some contemporaries said as much directly. It is also true that the decline of the trials in the Holy Roman Empire had several causes running at once, including the exhaustion of the Thirty Years War, changes in criminal procedure, the reassertion of higher courts over local ones, and a slow shift in what educated people found plausible. A book does not stop a persecution by itself.
Spee did not live to see any of it. He died in 1635 at Trier, of plague caught while nursing wounded soldiers, in his mid forties. His other surviving work is religious poetry, some of it still sung, which is not the usual afterlife for a man who wrote the sharpest procedural critique of his century.