The "traditional" method of catching moles, and by far the most humane, is by using traps that are designed to kill instantly. No poisons or gases are used so there is no unnecessary suffering to the animal.
There are traps available that are intended to take the mole alive. However moles have a very high metabolism and need to be constantly active and feeding, so these traps would need to be checked on an almost hourly basis to prevent the mole suffering a slow miserable death by starvation. There would also be the problem of what to do with a live mole as it is against the law to release a mammal into the wild. If it happened to be released into another mole’s territory, it could possibly result in a fight to the death!