Lots of possibilities on my mixer. Note that on my mixer a stereo signal can go to either two mono channels or one stereo channel. The following would apply to either.
Make sure of the cabling from the Axe FX outputs to the mixer inputs. Make sure you're actually running into to the mixer channel you think you are. I've screwed that up more than once.
Make sure the channel input gain is up.
Make sure the channel output fader is up.
Make sure the channel is assigned to the mixer main bus and/or an aux bus. I use the aux bus to route signals to my interface, my powered monitors are on the main bus.
Make sure the channel is not muted or some other channel is not soloed.
Make sure you don't have a muted series effect in the channel series fx insert. A parallel fx shouldn't matter, but turn down any fx bus sends just to be sure.
Just for debugging, set all your pans to center. Normally, you'll pan mono channels hard right and left, but a stereo channel would normally be panned center.
Make sure the mixer main bus and/or aux bus output fader is up. At this point you should see activity on the mixer output meter.
Make sure the mixer main or aux outputs are properly connected to an amp/speaker and that it's on.
Finally, or firstly, make sure the cables are good, and the mixer channel is good.