The myth goes something like this: If the queen’s wings are clipped she won’t be able to fly. If the queen is unable to fly, the swarm will return to the hive and stay with her.
In truth, the clipped queen may attempt to fly anyway, then fall to the ground and be unable to get back home. The swarm will return home briefly, but it will soon try again—often taking off with a recently hatched virgin queen.
In addition, clipped queens are often superseded more quickly than those with whole wings. The workers probably see these queens as “defective” and work to replace them as soon as possible. In other cases, clipped queens have been allowed to remain with no apparent consequence. You cannot tell in advance how the workers will react to an imperfect queen.
In any case, clipping is not nearly as popular as it once was. For a time, clipping was used as a way of dating the age of the queen. The right two wings were clipped on even years or the left two on odd years, but this practice has been replaced with a dot of colored paint or a number. Clipping performed by an inexperienced beekeeper can end in disaster, especially if the beekeeper accidentally nicks the thorax or snips a leg—so leave your queen intact and find some other way to reduce swarming.