The most humane way to remove an infestation of ground squirrels is by using live traps near the entrance of their nests to lure them out, then taking the traps to a further distance to release them in the wild. Fencing around areas such as gardens and plants that the animals would typically eat will also drive out the animals to search for another food source.
Flushing the squirrels out by flooding their nests with water will drive out the creatures and destroy their homes, ensuring that they cannot return, although this method has a chance of drowning and killing the young or those unable to escape. Putting bitter gels in the soil where the creatures would make their nests can also prevent the return once the nest is flushed out. The same method works with putting fox urine in the soil, as foxes are natural predators to the squirrels and the smell will alert them to avoid the area for fear of being hunted.
In most states, it is actually illegal to kill ground squirrels outside of the specific hunting seasons, so methods that are considered inhumane such as shooting and poisoning them are illegal. The squirrels also have senses that detect poison, alerting them to avoid the bait or area that has been poisoned.