You have a bunch of choices if you want to record the one Mic while playing live with others over the mixer.
1) Mic to Scarlett, Line out to Mixer: plug the Mic via XLR in the Scarlett, gain it there (with the high-quality preamp).
Important: activate the Direct Monitor switch which sends the gained input with nearly no latency to the outputs. This is important because you don't want latency when playing live with your other band members because if there is some latency, you will get sloppy.
Then take the normal Scarlett's line out to one of your mixers channel line in (you can/should use a TRS jack here for symmetric transmission).
You will then receive the line signal at the mixer and can mix it as you normally would. Probably, you won't need much gain at the mixer (if at all).
Pros: You use the high quality preamp to record your Mic.
Cons: If the scarlett crashes at some time when playing live, your signal won't reach the mixer and you won't be heard over the PA.
2) Mic to Mixer, monitor out to Scarlett: plug the Mic directly via XLR into one channel at the mixer. Gain it with the mixers gain and route it to one monitor output with the Aux1/Aux2 knobs. You should probably take the Aux1 (Pre) if possible to make the monitor send independable from the fader position. You will then receive the signal again at the desired Aux Output at the back. Then take this output and connect it to your Scarlett input (again, via TRS for symmetric transmission). You won't need to gain much (if at least) at the scarlett. You can then record the signal the normal way with your computer and have no need to worry about latency or failure of the Scarlett/computer (regarding the live playing).
Pros: If the scarlett crashes, you will hear no difference over the PA.
Cons: You are gaining with a lower-quality preamp.
3) Use the mixer's Insert I/O's: connect your mic directly to one of your mixer channels XLR input, gain it with the mixer. Now take a Y-cable (also known as input-cable which is: TRS/stereo jack at one end, two mono jacks at the other end) and put the stereo jack in the channel's Insert IO. You will then have your gained signal at the red (tip at the TRS) cable/jack and have to give it back with the white (ring at the TRS) cable/jack to the mixer. Now take a half-normalled patchbay and connect the red cable (Insert out) to the top plug on the patchbay's back, connect the white cable (Insert in) to the bottom plug on the patchbay's back.
At this point, your signal will simply be routed this way:
Mic->Preamp(Gain)->Insert out->Patchbay->Insert in->eq (normal mixer chain)...
But you will now have your gained signal once again (some kind of doubled) at the front top jack on the patchbay. Not connect a (important:) mono cable to the front top jack on the patchbay and connect it to your scarlett's input. You can then record it with your computer the normal way.
Pros: Easily customizable setup, you can leave everything set up and just need to plug in the cable between the Scarlett and the Patchbay if you want to record. Also, you won't block one monitor our (aux) just for recording. Again, if your Scarlett fails, this won't interrupt your live playing.
Cons: You are using the low-quality preamp of your mixer, you are transmitting the signal from the mixer (and patchbay) to your Scarlett non-symmetric which is bad when you use long cables or have interferences and should normally be avoided.