You have to look at the User Guide/Manual and specifications for the devices you wish to connect.
What plugs are on the mic? What ports are available one the Xbox and PC. What port options are offered on the mixer? Are you using 1/8" (3.5mm) jacks/ports? TR, TRS, TRRS?
The manuals are likely to list the required cables and plugs.
Some splitter may work....
My suggestion is to sketch out a simple diagram showing the devices and respective ports.
Map out the desired connections and check specs accordingly.
And, as another suggestion, take a look at the following website:
https://www.lifewire.com/stream-xbox-one-to-pc-4163361
Your streaming plans may be a bit more involved than expected.
Windows 10?
https://support.xbox.com/en-US/games/game-setup/how-to-use-game-streaming