You can control them when the adults fly (occurs in early spring, the exact time is variable to location), which happens for about 2 weeks. The large, overwintered worms emerge as tiny flies (sometimes mistaken for gnats) which will fly about, landing all over the boxwood plants.
There are a ton of effective chemicals you could use to knock them down, or you can use a dilution of soap and water, alcohol, neem oil, or another natural approach (which I recommend). Sometimes, people will use a systemic insecticide (the plant takes it in and circulates it throughout) which will also kill the feeding larvae.
About pruning, in many infestations, the pruning will often damage the plant more than the leaf miners will. If you do this, pick and choose, cutting out the worst infested areas, but try not to leave big holes. You really don't want to remove much, as the plants' health is already struggling as it is. To get rid of the growth, usually the larvae are underdeveloped in the trimmings, so you can usually just dry the clipping out in the sun, and the worms will die with the clippings. If you trim in early spring (after the worms have overwintered), there's a chance they will emerge.