抜く・切る: the difference
抜くN2
Meaning
All~, Completely, See through, Overcome, To the bitter end
Past papers
Tested 2 times in past papers
Example
ウォルターさんは化学のことなら知り抜いている。
Walter-san knows chemistry inside out.
切るN3
Meaning
To do something completely to the end, Utterly, Resolutely
Past papers
Tested once in past papers
Example
使い切ってから次のジャムを買ってよ。
Buy another jar of jam after you use one up completely.
How to tell them apart
「抜く」: pushing through pain and obstacles to the end. 「フルマラソンを走り抜いた」 (I ran the whole marathon).
「切る」: finishing completely with nothing left, or reaching an extreme. 「使い切る」 (use up), 「疲れ切る」 (be worn out), 「信じ切る」 (trust completely).
「通す」: keeping a belief or attitude unchanged from start to finish. 「初志を貫き通す」 (stick to the original aim), 「嘘をつき通す」 (keep up a lie to the end).