This is the 2495th most frequent Japanese word.
切る
"切る" means "to cut."
Here, '切る' conveys the action of cutting or severing something, in this case, paper.
紙を切る。
(I) cut the paper.
In this sentence, '切る' is used metaphorically to indicate interrupting or abruptly ending something.
話を途中で切らないでください。
Please do not interrupt (cut off) the conversation midway.
'切れる', the passive form of '切る', is used here to denote that something has been exhausted or finished.