In Act Two, John Proctor is infuriated when his wife, Elizabeth, is arrested for witchcraft. Herrick, an official of the courts, comes to his house with a written warrant to arrest Elizabeth. The charges are all based on Abigail's claim that Elizabeth had sent her spirit out to stab her; she even produced a needle from her belly to prove it. When the poppet is found in Elizabeth's house, that is all of the evidence that Herrick and the courts need to make good on the warrant and arrest Elizabeth then and there. John, who knows that this "evidence" is sketchy at best, and that Abby is behind all of it, having seen Mary put the needle in the doll, considers the arrest an atrocity and false. So, he grabs the warrant from Herrick and tears it up, as a statement of how it was false, and based upon a lie from Abigail.
This act of tearing up the warrant parallels his own tearing of his false confession in Act Four. John is pressured into confessing, falsely, to witchcraft. He signs the confession, and after he learns it will be posted on the church doors for the entire town to see, he has doubts. He knows that it is a lie, he knows the paper bears false witness against the truth and his reputation, and he knows that great harm will be done with that confession. So, in the end, he tears it up, because it is all a lie, just as he knew the warrant for Elizabeth's arrest was based on a lie.
These actions touch on the theme of hypocrisy, lying and deceit that run through the entire play. John was a constant advocate against deceipt, and his tearing of these two important documents symbolizes how his character tore through any falsity and exposed the real truth of matters. In his presence, lies did not stand. I hope that those thoughts helped; good luck.