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LingakuLingaku[verb ます-stem] + 切る
切る goes on a verb's ます-stem and means doing something all the way through, with nothing left: eating the whole cake, using up the money, running the full distance. It is often written in kana, たべ食べきる.
The verb is in the ます-stem, not the dictionary form: ×食べる切った. 切る itself conjugates as a う-verb: きった切った, きって切って, きれる切れる.
The potential きれる切れる says you can get through all of it, and the negative きれない切れない says there is too much to finish. The negative is the form you meet most.
These go beyond finishing an action.
On verbs of feeling or condition, 切る means the state has gone as far as it can: "utterly", "completely".
A few compounds with verbs of saying and deciding mean doing it flatly, without hedging. いいきる言い切る is "state flatly", and おもいきる思い切る is "make up your mind".