To Tear Up
To Tear Off, To Split
transitive verb, godan verb
You know that 裂く is "to tear" or "to rip up." So, if you're trying to tear or rip up something, and you're pulling it at the same time, you are going to tear up that thing, or more accurately perhaps to tear off something, since you're pulling.
The reading comes from 引く and 裂く.
あのカップルの仲をうまく引き裂く事ができたら、お知らせ致します。
I’ll let you know if I succeed in splitting up the couple.