To be honest, I'm not close to competent in Korean enough to know, having only been learning the language for three years (not Taekwondo terms, but actually learning Korean). I'm only an intermediate speaker/reader/writer and an awful listener ;-)
The simple dictionary translation of kyukpa/격파 means destruction/annihilation. However, that doesn't mean that destruction/annihilation of the target is the only criteria. For example, a nuclear missile's purpose is to obliterate a target and to leave a long last post-impact devastation effect. That doesn't mean you can't have a successful nuclear missile test without obliterating a target (e.g if you aim at sea, it will have a temporary effect, but maybe not obliteration of that area of the sea because the water will flood/fall back immediately).
For example, most people translate kyeorugi/겨루기 as "fighting" or "sparring", but in fact it just means "competing or matching ones strength with the opponent". And that's from my Mac's built in dictionary (kyeoruda/겨루다 the verb which it comes from), I'm sure if I understood enough Korean, I could research the etymology of the word, but there's certainly more to it than a word word answer or simple concept.
Similar to how Tae-kwon-do is often translated as "foot-fist-way", but each word has a much larger conceptual meaning than that (which I'm not going to bother typing out).
So, regardless of what the literal translation of breaking or kyukpa is, you have to look for the wider context of why you're doing it, what it means in the context of Taekwondo and therefore determine your success criteria for your students (when you're a high enough grade to have them and promote them).