You can connect send sound out an amp and to a mixer. If you have 4 outs on your audio interface you could send one set of cables to the amp, one set of cables to the mixer.
If you are using Sunday Guitar you might want to experiment with the direct and transparent preamp models in the speaker/amps section. That will bypass the amp modeling in MainStage for that channel. Sometimes the amp models sound okay when running into a real amp though so we would suggest that you experiment there.