〜抜きで・〜抜きには
without, leaving out
Noun + 抜きで / 抜きに / 抜きの · 抜きには + negative
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抜きで means leaving out something that would normally be included: 朝ご飯抜きで学校に行った, "I went to school without breakfast". 抜く means "to pull out".
At a restaurant, it's how you ask to leave out an ingredient: わさび抜きでお願いします, "no wasabi, please".
The set phrase 冗談抜きで means "joking aside, seriously".
抜きには with a negative stresses that something is essential: 彼抜きには、この計画は成功しなかった, "this plan wouldn't have succeeded without him". 堅い話は抜きにして means "let's skip the serious talk".
It's close to なしで, but 抜き suggests removing something that's usually there.
Examples
朝ご飯抜きで、学校に行った。
I went to school without breakfast.
冗談抜きで、本当に困っているんです。
Joking aside, I'm really in trouble.
わさび抜きでお願いします。
No wasabi, please.
彼抜きには、この計画は成功しなかった。
This plan wouldn't have succeeded without him.
堅い話は抜きにして、楽しみましょう。
Let's skip the serious talk and just have fun.