This pattern means 'without (doing) X' or 'setting aside X', and it is used when you want to emphasize that something is done directly, without the usual preliminaries or considerations. It often appears in expressions like 冗談抜きにして (jokes aside) or 前置き抜きにして (without preamble). When the noun is an action, it can imply skipping that action entirely, like 議論抜きにして (without discussion).

A common use is with は to say 'without X, (something else) is impossible/doesn't happen': (noun) 抜きにしては + negative or potential form. For example, 彼女抜きにしては成功しなかった (without her, we wouldn't have succeeded). This pattern is rather formal and often found in speeches or written Japanese, but also used in everyday conversation with set phrases.

In speech, you might hear 抜きで instead, which is lighter and more colloquial: 前置き抜きで話そう (let's talk without preamble). But 抜きにして is fine in both spoken and written when you want a bit of weight.