if you’re going to catch-release ground squirrels check your local and state laws. Some say min of 5 miles away some say no dumping live squirrels anywhere.
The most humane way is a BB air pistol or kid’s Daisy bbgun behind the ear or at the base of the skull/spine. Use a stick through the cage to nudge the critter into a corner and hold it down if it’s not fear-frozen already. And use eye protection since you’ll be shooting at close range. Or, you can dunk the cage in a water barrel and come back in 30 minutes. They drown pretty fast. After finding a drowned one vertical in the corral water barrel (he couldn’t climb the wet surface) we figured drowning must be pretty terrifying so we prefer the bb’s. One shot (hopefully), one kill, one second.
And if you’re feeling squeamish about the above, just remember that hawks, owls and ravens eat them alive and so do rattlers, boas and feral cats, which we also have our fair share of, so a quick death really is the most humane.
Thanks