The book was published without its author's name, at Rinteln in 1631, and the precaution was sensible. It accused named practices, and by clear implication the princes, judges and clergy who ran them, of killing innocent people in numbers. Spee's authorship was known in his lifetime nonetheless, and Leibniz affirmed it later in the century.
What it achieved is honestly uncertain. Historians credit the Cautio with contributing to the ending of prosecutions in several German territories, and some contemporaries said so directly. It is also true that the decline in the Holy Roman Empire had several causes running together: the exhaustion of the Thirty Years War, reform of criminal procedure, higher courts reasserting review over local ones, and a slow change in what educated men were prepared to believe. A book does not stop a persecution on its own, and nobody has isolated its effect.
Spee saw none of it. He was seriously injured in an attack in 1629, and in 1635 he died at Trier of plague caught while nursing wounded soldiers, in his mid forties. His other surviving work is devotional poetry, published after his death, some of which is still sung in German hymnals at Christmas.
It is worth holding those two things together. The sharpest procedural critique of the seventeenth century and a set of tender Christmas carols were written by the same man, out of the same conviction, in the same short life.