抜（ぬ）きで, a combination of the noun form of the う-Verb 抜（ぬ）く ‘to extract’, and the particle で, is a construction that usually indicates something being done ‘without (A)’, or ‘with the removal of (A)’. As ぬき indicates the extraction of something, this grammar pattern is primarily used to indicate ‘leaving out’, or ‘setting aside’ something that is regularly included.
抜（ぬ）きで acts as a suffix, so will be utilized after nouns, to indicate the thing that is being left out. Both the plain hiragana and kanji forms are fairly common. Additionally, の will replace で when ぬき is followed directly by another noun.

• あの人（ひと）は冗談（じょうだん）抜（ぬ）きで怖（こわ）いから怒（おこ）らせない方（ほう）がいいよ。
  That guy is scary, no joke, so you shouldn't upset him.
• あいつら全然（ぜんぜん）来（こ）ないな、あいつら抜（ぬ）きで始（はじ）めちゃおうぜ。
  They aren’t coming at all (it doesn't seem like they are coming anytime soon). Let’s start without them.
• サビ抜（ぬ）きの寿司（すし）なんて寿司（すし）じゃないよ。
  Sushi without wasabi is not sushi.

Occasionally, にして may also replace で, but this is structure is more common when the part (B) section of the sentence includes a ない or できない based statement. These expressions indicate that something ‘will not happen without (A)’, or ‘is not possible without (A)’.

• 若（わか）い労働者（ろうどうしゃ）抜（ぬ）きにしては、日本（にほん）の建築業（けんちくぎょう）は成（な）り立（た）たない。
  Without young workers, Japan's construction industry would not exist.
• 公共（こうきょう）交通（こうつう）機関（きかん）抜（ぬ）きにしては便利（べんり）な生活（せいかつ）ができない。
  Without public transportation, you cannot live a convenient life.

However; this is not always the case, as ぬきで or ぬきでは may also appear in negative sentences, with the same meaning.