To be quick-witted and mentally sharp; to be clever and able to think or decide quickly.
彼は交渉で相手の弱点をすぐ見抜く。頭が切れる人だ。
He immediately spots the other side's weak points in negotiations. He's a sharp-minded person.
頭が切れるので、短い時間で問題の解決策を出してくれた。
Because she's quick-witted, she came up with a solution to the problem in a short time.
あの記者は頭が切れるから、鋭い質問をたくさんする。
That reporter is sharp, so he asks a lot of pointed questions.
頭が切れる人は状況を素早く整理して優先順位を決められる。
A sharp person can quickly sort out a situation and decide priorities.