"If I bend that far, I will break."
"bend" is 휘다 or 구부러지다/굽다 (intransitive) or 굽히다/구부리다 (transitive).
So a strict translation would be 그렇게까지 휘다간 부러진다 or 그겋게 너무 굽히다간 부러진다.
But as a metaphor for "bending over backward" or "overextending", Koreans don't seem to use the same "bend and break" expression. I can't think of widely used expression for that other than 너무 나가다간 다친다 (you'll get hurt if you go too far).
For bending and breaking, there is a different but related popular saying which means "if you don't bend you'll break" ("Don't be too inflexible"):
휘지 않으면 부러진다 / 구부러지지 않는 것은 부러진다.