しまう - completion (and ending up in a certain condition) or indicating strong feelings such as regret or remorse.
もう荷造りしてしまった。- I packed my bags (and it is done!).
ケーキをすべて食べてしまった。He ate the whole damn cake! (Anger? Impressed?)
タバコをやめてしまう!- I'm going to give up smoking! (determination)
きる - to do something completely, thoroughly, sufficiently, strongly and or, borrowing from the actual meaning of 切る, an idea of severance - discarding or giving up
もう荷造りしきった。- I packed my bags (speaker is determined to go or packed to cover any contingency)
離れてからも彼女のことを思いきることができない - Even since we broke up, I can't stop thinking (cut off my thoughts) about her.