This question is prompted by the earlier question on the use of 書ける. Initially I thought the answer might explain the difference between these two (eg 彼は頭がよく切れる| he is (very) sharp) but in most cases, including this one the adjective seems unnecessary. (For reference, I have made a list of common examples below.)
(Also, as an observation, because I don't want to over-extend the scope of the question 切れる also seems to be used in compound verbs while 切り is used in compound "masu-形 nouns" such as 締め切り/deadline or 思い切り/to one's content.)
Examples of 切れる:
ひもが切れる| the string breaks
電池が切れる| the battery dies
たばこが切れる| be out of cigarettes
賞味期限が切れる| past best before date
しびれが切れる (=足がしびれる)| legs have gone to sleep
彼は頭が(よく)切れる| he is (very) sharp
Examples of 切る:
電源を切る| switch off
野菜の水気を切る drain water from vegetables
スタートを切る| start off
100メートル競走で10秒を切る| run 100m in less than 10 secs
ハンドルを右に切る| turn the wheel to the right
カードをよく切る| Please shuffle the cards well. |
キレて、犯罪を犯す若者が増加している|
The number of young people committing crimes as a result of rage is increasing.
Examples of compund verbs with 切れる:
チケットが売り切れる| tickets are sold out
だれがそれを言い切れるだろうか| who would dare to say that with (any) certainty?
会話が 途切れる (とぎれる)| the conversation comes to a halt