Asunder is an adverb that means “into separate pieces.” So if you’ve torn your ex's love letter asunder, you’ve forcefully ripped it into separate pieces — and rightly so.
Asunder comes from the Old English phrase on sundran, which means "into separate places." It is a somewhat archaic and uncommon word and many people know it only from religious marriage ceremonies: "What God has joined together let no man put asunder." In most cases, you can use its more common synonym "apart" and convey the same meaning, unless you want to express a particularly violent or forceful ripping.